Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
186 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21447700 | C2 | semidirect |
| 2. #21444023 | C2 | semidirect |
| 3. #21444003 | C2 | semidirect |
| 4. C32×Dic61 | C2 | semidirect |
| 12. C61×Q64 | C4 | semidirect |
| 13. C61×SD64 | C4 | semidirect |
| 14. C61×D32 | C4 | semidirect |
| 70. Q64 | Dic61 | semidirect |
| 71. SD64 | Dic61 | semidirect |
| 72. D32 | Dic61 | semidirect |
| 78. C61 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447700 | 2 |
| #21444023 | 2 |
| #21444003 | 2 |
| C32×Dic61 | 2 |
| C61×#2262 | 2 |
| #13655 | 61 |