Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
578 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 116 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. #21462000 | C2 | semidirect |
| 4. #21461946 | C2 | semidirect |
| 5. #21461754 | C2 | semidirect |
| 6. #21461015 | C2 | semidirect |
| 20. #16840110 | C4 | semidirect |
| 21. #16840109 | C4 | semidirect |
| 22. #16840108 | C4 | semidirect |
| 26. C61×#486 | C4 | semidirect |
| 218. #486 | #6923 | semidirect |
| 231. C61 | #9827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462000 | 2 |
| #21461947 | 2 |
| #21461946 | 2 |
| #21461754 | 2 |
| #21461015 | 2 |
| #486×D61 | 2 |
| #9827 | 61 |