Belongs within: Cerithiimorpha.
Clava is another genus of small high-spired marine gastropods similar to Cerithium. (I think that this genus may be no longer considered valid; some of my references are a little dated.)
Characteristics (from Compton 1944): Parietal callus free, not attached to body whorl; evenly distributed, nearly cancellate ornamentation; ridgelike disc present on basal whorl; shell angular, penultimate whorl not decidedly enlarged; anterior canal well-developed.
<==Clava |--C. aluco (Linnaeus 1758) [=Murex aluco]H09 |--C. aspera (Linnaeus 1758) [=Murex asper]H09 |--C. bidentata [=Cerithium (Clava) bidentata]F27 | |--C. b. bidentataF27 | `--C. b. schafferi Finlay 1927 (see below for synonymy)F27 |--C. nodulosa Bruguière 1792H09 |--C. pulchra (Sowerby 1855) [=Vertagus pulcher]H09 |--C. recurva (Sowerby 1855) [=Cerithium recurvum]H09 |--C. sinensis (Gmelin 1791) [=Murex sinensis, Cerithium obeliscus Bruguière 1792]H08 `--C. sowerbyi (Kiener 1842) [=Cerithium sowerbyi]H09
Clava bidentata schafferi Finlay 1927 [=Cerithium (Clava) bidentata var. abbreviata Schaffer 1912 nec Cerithium abbreviatum Leckenby 1858 nec Brazier 1877]F27
*Type species of generic name indicated
References
Compton, R. R. 1944. A new Paleocene gastropod from southern California. Journal of Paleontology 18 (5): 464–469.
[F27] Finlay, H. J. 1927. New specific names for austral Mollusca. Transactions and Proceedings of the New Zealand Institute 57: 488–533.
[H08] Hedley, C. 1908. Studies on Australian Mollusca. Part X. Proceedings of the Linnean Society of New South Wales 33: 456–489, pls 7–10.
[H09] Hedley, C. 1909. The Marine Fauna of Queensland: Address by the President of Section D. Australasian Association for the Advancement of Science: Brisbane.