Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 119 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. #21447430 | C2 | semidirect |
| 2. #21445536 | C2 | semidirect |
| 3. #21443828 | C2 | semidirect |
| 8. C22⋊#11758185 | C22 | semidirect |
| 10. #16839525 | C22 | semidirect |
| 11. C22×D8×C61 | C4 | semidirect |
| 16. C61×#466 | C4 | semidirect |
| 18. C2×#107×C61 | C4 | semidirect |
| 161. C22×D8 | Dic61 | semidirect |
| 168. #466 | Dic61 | semidirect |
| 170. C2×#107 | Dic61 | semidirect |
| 176. C61 | #11705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447430 | 2 |
| #21445536 | 2 |
| #21443828 | 2 |
| C2×C61×#466 | 2 |
| #11705 | 61 |