Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
522 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 522 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. #21461997 | C2 | semidirect |
| 3. C8×C4⋊#6923 | C2 | semidirect |
| 4. D61⋊#334 | C2 | semidirect |
| 5. D61⋊#333 | C2 | semidirect |
| 22. #16840110 | C4 | semidirect |
| 23. #16840109 | C4 | semidirect |
| 24. #16840108 | C4 | semidirect |
| 30. C61×#486 | C4 | semidirect |
| 227. #486 | #6923 | semidirect |
| 243. C61 | #9735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461997 | 2 |
| #21461986 | 2 |
| C8×C4⋊#6923 | 2 |
| D61⋊#334 | 2 |
| D61⋊#333 | 2 |
| D61⋊#331 | 2 |
| #486×D61 | 2 |
| #9735 | 61 |