Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1014 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 192 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. #21462578 | C2 | semidirect |
| 2. #21461980 | C2 | semidirect |
| 3. #21461826 | C2 | semidirect |
| 4. #21461621 | C2 | semidirect |
| 17. #16840139 | C4 | semidirect |
| 18. #16840138 | C4 | semidirect |
| 19. #16840137 | C4 | semidirect |
| 21. C61×#493 | C4 | semidirect |
| 28. #14519846 | D4 | semidirect |
| 29. #14519845 | D4 | semidirect |
| 36. C2×D488 | C2×C4 | semidirect |
| 37. C2×#11758199 | C2×C4 | semidirect |
| 43. #14519774 | C2×C4 | semidirect |
| 45. #14519773 | C2×C4 | semidirect |
| 47. C4×#92418 | C2×C4 | semidirect |
| 48. C8×Dic61 | C2×C4 | semidirect |
| 49. C2×D8×C61 | C2×C4 | semidirect |
| 50. #127×C61 | C2×C4 | semidirect |
| 51. C4×C8×C61 | C2×C4 | semidirect |
| 146. #493 | #6923 | semidirect |
| 156. C61 | #23201 | semidirect |
| 165. C2×D8 | C2×#6923 | semidirect |
| 171. #127 | C2×#6923 | semidirect |
| 186. C4×C8 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462578 | 2 |
| #21461980 | 2 |
| #21461826 | 2 |
| #21461621 | 2 |
| #493×D61 | 2 |
| #23201 | 61 |