Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
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. #21458957 | C2 | semidirect |
| 2. #21457619 | C2 | semidirect |
| 3. #21448069 | C2 | semidirect |
| 4. #21447940 | C2 | semidirect |
| 5. #21447895 | C2 | semidirect |
| 6. #21447777 | C2 | semidirect |
| 7. #21447657 | C2 | semidirect |
| 8. C61×#2178 | C2 | semidirect |
| 10. #16840564 | C22 | semidirect |
| 12. #16840197 | C22 | semidirect |
| 14. C2×D976 | C22 | semidirect |
| 15. C2×D976 | C22 | semidirect |
| 17. #16840178 | C22 | semidirect |
| 18. #16840139 | C22 | semidirect |
| 19. #16840033 | C22 | semidirect |
| 23. #16839583 | C22 | semidirect |
| 24. #16839574 | C22 | semidirect |
| 25. #16839545 | C22 | semidirect |
| 27. C61×#443 | C22 | semidirect |
| 28. C61×#368 | C22 | semidirect |
| 29. C61×#359 | C22 | semidirect |
| 30. C4×C16×C61 | C22 | semidirect |
| 58. Q32×C61 | D4 | semidirect |
| 59. SD32×C61 | D4 | semidirect |
| 60. D16×C61 | D4 | semidirect |
| 144. #2178 | D61 | semidirect |
| 166. #443 | C2×D61 | semidirect |
| 167. #368 | C2×D61 | semidirect |
| 170. #359 | C2×D61 | semidirect |
| 172. C4×C16 | C2×D61 | semidirect |
| 173. C61 | #33858 | semidirect |
| 190. Q32 | D244 | semidirect |
| 192. SD32 | D244 | semidirect |
| 197. D16 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458957 | 2 |
| #21457619 | 2 |
| #21448069 | 2 |
| #21447940 | 2 |
| #21447895 | 2 |
| #21447777 | 2 |
| #21447657 | 2 |
| C61×#2178 | 2 |
| #33858 | 61 |