Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 3. #21443978 | C2 | semidirect |
| 7. C2×#14519777 | C4 | semidirect |
| 8. #16840157 | C4 | semidirect |
| 13. C4×#11758194 | C4 | semidirect |
| 168. C61 | #13580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456279 | 2 |
| #21447504 | 2 |
| #21443978 | 2 |
| C61×#2126 | 2 |
| #13580 | 61 |