Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. C2×#16839559 | C2 | semidirect |
| 3. #21443978 | C2 | semidirect |
| 4. #21443975 | C2 | semidirect |
| 5. C2×C61×#354 | C2 | semidirect |
| 8. #16840312 | C4 | semidirect |
| 9. #16840157 | C4 | semidirect |
| 11. #16840152 | C4 | semidirect |
| 16. C4×#11758194 | C4 | semidirect |
| 38. #14519777 | C2×C4 | semidirect |
| 39. #14519774 | C2×C4 | semidirect |
| 45. #14519688 | C2×C4 | semidirect |
| 46. #14519688 | C2×C4 | semidirect |
| 172. C2×#354 | D61 | semidirect |
| 199. C61 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456283 | 2 |
| C2×#16839559 | 2 |
| #21443978 | 2 |
| #21443975 | 2 |
| C2×C61×#354 | 2 |
| #13578 | 61 |