Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 90 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. #21461983 | C2 | semidirect |
| 2. #21461982 | C2 | semidirect |
| 3. C4×#14519845 | C2 | semidirect |
| 4. #21461200 | C2 | semidirect |
| 5. #21461199 | C2 | semidirect |
| 6. #21461029 | C2 | semidirect |
| 22. #16840165 | C4 | semidirect |
| 23. #16840138 | C4 | semidirect |
| 24. #16840109 | C4 | semidirect |
| 30. C61×#486 | C4 | semidirect |
| 171. #92418 | #104 | semidirect |
| 214. #486 | #6923 | semidirect |
| 232. C61 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461983 | 2 |
| #21461982 | 2 |
| C4×#14519845 | 2 |
| #21461200 | 2 |
| #21461199 | 2 |
| #21461029 | 2 |
| #21456397 | 2 |
| #9721 | 61 |