Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21454736 | C2 | semidirect |
| 2. C2×#16839575 | C2 | semidirect |
| 3. #21447547 | C2 | semidirect |
| 4. #21446730 | C2 | semidirect |
| 5. #21443923 | C2 | semidirect |
| 6. #21443904 | C2 | semidirect |
| 24. C2×SD32×C61 | C4 | semidirect |
| 25. C2×D16×C61 | C4 | semidirect |
| 183. C2×SD32 | Dic61 | semidirect |
| 184. C2×D16 | Dic61 | semidirect |
| 197. C61 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454736 | 2 |
| C2×#16839575 | 2 |
| #21447547 | 2 |
| #21446730 | 2 |
| #21443923 | 2 |
| #21443904 | 2 |
| C2×C61×#509 | 2 |
| #13036 | 61 |