Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
618 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 106 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. #21462348 | C2 | semidirect |
| 4. D61⋊#332 | C2 | semidirect |
| 5. #21460654 | C2 | semidirect |
| 6. #21460654 | C2 | semidirect |
| 24. #16840110 | C4 | semidirect |
| 25. #16840109 | C4 | semidirect |
| 26. #16840108 | C4 | semidirect |
| 30. C61×#486 | C4 | semidirect |
| 272. #486 | #6923 | semidirect |
| 288. C61 | #9062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462348 | 2 |
| #21461986 | 2 |
| D61⋊#332 | 2 |
| #21460654 | 2 |
| #486×D61 | 2 |
| #9062 | 61 |