Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 11. #16840603 | C4 | semidirect |
| 12. C8×#92420 | C4 | semidirect |
| 15. #16839484 | C4 | semidirect |
| 16. C8×#92418 | C4 | semidirect |
| 17. C82×C61 | C4 | semidirect |
| 23. #14519831 | C8 | semidirect |
| 105. C82 | #6923 | semidirect |
| 106. C61 | #8138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461475 | 2 |
| #21461023 | 2 |
| #21460644 | 2 |
| #21460642 | 2 |
| #21444101 | 2 |
| #8138 | 61 |