Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
352 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 78 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. #21462183 | C2 | semidirect |
| 2. C4×#14519846 | C2 | semidirect |
| 3. #21460807 | C2 | semidirect |
| 13. #16840164 | C4 | semidirect |
| 18. Q16×Dic61 | C4 | semidirect |
| 20. D8×Dic61 | C4 | semidirect |
| 22. C61×#495 | C4 | semidirect |
| 155. #495 | #6923 | semidirect |
| 170. C61 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462183 | 2 |
| C4×#14519846 | 2 |
| #21460807 | 2 |
| #21460805 | 2 |
| #21456386 | 2 |
| #11746 | 61 |