Belongs within: Hyolitha.
The Hyolithidae were a family of hyoliths found during the Cambrian and Ordovician. Though the circumscription of the family has varied widely over the years (and the type genus, Hyolithes, seems to have long been the default repository for almost any hyolith), it was defined by Kruse (2002) as including those species in which a ligula is present on the venter, and the dorsoventral transition is decoupled from the lateral transition such that the venter perimeter is greater than the dorsal perimeter. Helenia was named for tubular fossils that in fact represent isolated struts from large hyolithids (Fisher 1962).
Malinky (2002) indicated that Hyolithes should be restricted to species possessing a lateral furrow near each edge of the dorsum. He also classified the genera Diplotheca and Camerotheca within the Hyolithidae (the latter as a synonym of Hyolithes). These two genera had previously been classified separately on the basis of the structure of the shell apex, which was supposed to be cylindrical and septate rather than simply conical as in Hyolithidae, but Malinky (1990) demonstrated that these supposed characters were not visible in the original specimens.
<==Hyolithidae [Camerothecida, Camerothecidae, Camerothecina, Diplothecida, Diplothecidae, Diplothecina]
|--Novakotheca Malinky 1990M02
|--Raitilites Marek 1989K02
|--Hallotheca Malinky, Linsely & Yochelson 1987M02
|--Korilithes Missarzhevsky 1969M02
|--Karlithes bilabiatus Missarzhevsky 1969W93
|--Yalarrnga Kruse 2002K02
| `--*Y. mara Kruse 2002K02
|--Diplotheca Matthew 1885 non Hochst. 1846 (ICBN)M90
| `--*D. hyattiana Matthew 1885 [=Hyolithes hyattianus; incl. D. hyattiana var. caudata Matthew 1885, H. caudatus]M90
|--Helenia Walcott 1889DJ71
| `--*H. bella Walcott 1889F62
|--Joachimilites Marek 1967K02
| |--J. modestusMMB05
| `--J. novaki Marek 1967Y84
|--Sololites Marek 1967K02
| |--*S. ferrigenus Marek 1967K02
| `--S. kankari Kruse 2002K02
|--Haplophrentis Babcock & Robison 1988MSC17
| |--H. carinatus (Matthew 1899)MSC17 [=Hyolithes carinatusM90]
| `--H. reesei Babcock & Robison 1988MSC17
|--Carinolithes Syssoiev 1958M02
| |--*C. pennatulus (Holm 1893) [=Hyolithus pennatulus]M02
| |--C. hospes (Holm 1893) [=Hyolithes hospes, Hyolithes hospe (l. c.), Hyolithus (l. c.) hospes]M02
| |--‘Hyolithus’ pennatuloides Cobbold & Pocock 1934M02
| |--C. tantulus Marek 1967M02
| |--C. tjikilirri Kruse 2002K02
| `--C. triumvir (Holm 1893) [=Hyolithes triumvir, Hyolithus (l. c.) triumvir]M02
`--Hyolithes Eichwald 1840M02 (see below for synonymy)
|--*H. acutus Eichwald 1840M02
|--H. acadica Hartt in Walcott 1884 (see below for synonymy)M90
|--H. americanus Billings 1872MB-M99
|--H. angustusM02
|--H. ardmillanensisM02
|--H. attenuatus Walcott 1890M02
|--H. balticus Poulsen 1967MB-M99
|--H. bicostatus Novák 1891M02
|--H. bisulcatus Holm 1893 [=Hyolithus (l. c.) bisulcatus]M02
|--H. communis Tate 1892K02 [=Aimitus communisMB-M99]
|--H. concinnus Holm 1893 [=Hyolithus (l. c.) concinnus]M02
|--H. confusus Holm 1893 [=Hyolithus confusus]MB-M99
|--H. conularoides Tate 1892K02
|--H. corrugatus Kiaer 1916MB-M99
|--H. costatus Matthew 1901M90
|--H. costulatus Barrande 1867M02
|--H. degeeri Holm 1893M02 [=Hyolithus (Orthotheca) degeeriMB-M99, Allatheca degeeriMB-M99, Mooritheca degeeriMB-M99]
|--H. giganteusMMB05
|--H. gracilior Matthew 1895M90
|--H. gracilis Matthew 1885 [=Hyolithes (*Camerotheca) gracilis]M90
|--H. gracillimus Matthew 1901M90
|--H. gregariaW77
|--H. hathewayiF62
|--H. hermelini Holm 1893 [=Hyolithus (Orthotheca) hermelini, Circotheca hermelini]MB-M99
|--H. incurvatus Novák 1891M02
|--H. innotatus Holm 1893 [=Hyolithus (l. c.) innotatus]M02
|--H. kirkbyi (Howse 1857) [=Theca kirkbyi]W93
|--H. lanceolatus (Morris 1845) [=Theca lanceolatus]F62
|--H. latus Eichwald 1860 [incl. H. latus var. recidivus]M02
|--H. lenticularis Holm 1893 [=Hyolithus lenticularis, Linevitus lenticularis]MB-M99
|--H. lineatus Kjerulf 1865M02
|--H. lineolatus Salter in Salter & Blandford 1865M02
|--H. magnificusF62
|--H. micmac Matthew in Walcott 1884 [=H. (Camerotheca) micmac, H. (Orthotheca) micmac]M90
|--H. mimicus Cobbold 1931MB-M99
|--H. nathorsti Johnstrup in Holm 1893MB-M99
|--H. norvegicus Kjerulf 1865 [incl. Theca elegantula Kjerulf 1865]M02
|--H. obesus Holm 1893 (n. d.) [=Hyolithus obesus, Dorsolinevitus obesus]MB-M99
|--H. orientalis Waagen 1880PY84
|--H. plicatus Brøgger 1878MB-M99
|--H. poulseni Resser 1938M02
|--H. primordialis (Hall 1861) [=Theca primordialis]W77
|--H. triangularis Portlock 1843M02
`--H. tricarinatusF62
Nomina nuda: Camerotheca snajdri Syssoiev 1962M90
Hyolithes broeggeri Holm 1893MB-M99
Hyolithes Eichwald 1840M02 [=Hyolithus (l. c.)M02; incl. Camerotheca Matthew 1885M90, Centrotheca Salter 1866F62, Cleidotheca Salter 1866F62, Cleodora Ludwig 1864 nec Péron & Lesueur 1810 nec Mulsant 1850F62, Orthoceras Münster 1840 non Bruguière 1789F62, Pugiunculus Barrande 1847F62, Vaginella d’Orbigny 1850 non Daudin 1800F62]
Hyolithes acadica Hartt in Walcott 1884 [=Diplotheca acadica, Theca acadica; incl. D. a. var. crassa Matthew 1885, Hyolithes crassus, D. a. var. obtusa Matthew 1886, D. a. var. sericea Matthew 1886, Hyolithes sericeus]M90
*Type species of generic name indicated
References
[DJ71] Druce, E. C., & P. J. Jones. 1971. Cambro-Ordovician conodonts from the Burke River Structural Belt, Queensland. Commonwealth of Australia, Bureau of National Development, Bureau of Mineral Resources, Geology and Geophysics, Bulletin 110: 1–159.
[F62] Fisher, D. W. 1962. Small conoidal shells of uncertain affinities. In: Moore, R. C. (ed.) Treatise on Invertebrate Paleontology pt W. Miscellanea: Conodonts, Conoidal Shells of Uncertain Affinities, Worms, Trace Fossils and Problematica pp. W98–W143. Geological Society of America, and University of Kansas Press.
[K02] Kruse, P. D. 2002. Biostratigraphic potential of Middle Cambrian hyoliths from the eastern Georgina Basin. Alcheringa 26: 353–398.
[M90] Malinky, J. M. 1990. Cambrian Hyolitha from northeast Canada: reappraisal of the hyolith orders Camerothecida and Diplothecida. Journal of Paleontology 64 (4): 587–595.
[M02] Malinky, J. M. 2002. A revision of Early to Mid Ordovician hyoliths from Sweden. Palaeontology 45: 511–555.
[MMB05] Martí Mus, M., & J. Bergström. 2005. The morphology of hyolithids and its functional implications. Palaeontology 48 (6): 1139–1167.
[MSC17] Moysiuk, J., M. R. Smith & J.-B. Caron. 2017. Hyoliths are Palaeozoic lophophorates. Nature 541: 394–397.
[PY84] Peel, J. S., & E. L. Yochelson. 1984. Permian Toxeumorphorida from Greenland: an appraisal of the molluscan class Xenoconchia. Lethaia 17: 211–221.
[W77] White, C. A. 1877. Report upon the invertebrate fossils collected in portions of Nevada, Utah, Colorado, New Mexico, and Arizona, by parties of the expeditions of 1871, 1872, 1873, and 1874. U.S. Geographical Surveys West of the One Hundredth Meridian 4 (1): 1–219, pls 1–21.
[W93] Wills, M. A. 1993. ?Mollusca incertae sedis. In: Benton, M. J. (ed.) The Fossil Record 2 pp. 265–270. Chapman & Hall: London.
[Y84] Yochelson, E. L. 1984. Speculative functional morphology and morphology that could not function: the example of Hyolithes and Biconulites. Malacologia 25 (1): 255–264.