Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21437234 | C2 | semidirect |
| 2. #21435896 | C2 | semidirect |
| 3. #21426346 | C2 | semidirect |
| 4. #21426217 | C2 | semidirect |
| 5. #21426172 | C2 | semidirect |
| 6. #21426054 | C2 | semidirect |
| 7. #21425934 | C2 | semidirect |
| 8. C59×#2178 | C2 | semidirect |
| 10. #16838204 | C22 | semidirect |
| 12. #16837837 | C22 | semidirect |
| 14. C2×D944 | C22 | semidirect |
| 15. C2×D944 | C22 | semidirect |
| 17. #16837818 | C22 | semidirect |
| 18. #16837779 | C22 | semidirect |
| 19. #16837673 | C22 | semidirect |
| 23. #16837223 | C22 | semidirect |
| 24. #16837214 | C22 | semidirect |
| 25. #16837185 | C22 | semidirect |
| 27. C59×#443 | C22 | semidirect |
| 28. C59×#368 | C22 | semidirect |
| 29. C59×#359 | C22 | semidirect |
| 30. C4×C16×C59 | C22 | semidirect |
| 58. Q32×C59 | D4 | semidirect |
| 59. SD32×C59 | D4 | semidirect |
| 60. D16×C59 | D4 | semidirect |
| 144. #2178 | D59 | semidirect |
| 166. #443 | C2×D59 | semidirect |
| 167. #368 | C2×D59 | semidirect |
| 170. #359 | C2×D59 | semidirect |
| 172. C4×C16 | C2×D59 | semidirect |
| 173. C59 | #33858 | semidirect |
| 190. Q32 | D236 | semidirect |
| 192. SD32 | D236 | semidirect |
| 197. D16 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437234 | 2 |
| #21435896 | 2 |
| #21426346 | 2 |
| #21426217 | 2 |
| #21426172 | 2 |
| #21426054 | 2 |
| #21425934 | 2 |
| C59×#2178 | 2 |
| #33858 | 59 |