Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#16839869 | C2 | semidirect |
| 2. C2×#16839578 | C2 | semidirect |
| 5. #21443918 | C2 | semidirect |
| 6. #21443898 | C2 | semidirect |
| 24. C2×Q32×C61 | C4 | semidirect |
| 25. C2×SD32×C61 | C4 | semidirect |
| 182. C2×Q32 | Dic61 | semidirect |
| 183. C2×SD32 | Dic61 | semidirect |
| 196. C61 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839869 | 2 |
| C2×#16839578 | 2 |
| C2×#16839572 | 2 |
| #21446713 | 2 |
| #21443918 | 2 |
| #21443898 | 2 |
| C2×C61×#510 | 2 |
| #13038 | 61 |