Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 8. #16840813 | C4 | semidirect |
| 11. Q8×#92420 | C4 | semidirect |
| 26. #16839511 | C4 | semidirect |
| 27. #16839509 | C4 | semidirect |
| 28. #16839507 | C4 | semidirect |
| 29. C61×#333 | C4 | semidirect |
| 185. #333 | #6923 | semidirect |
| 191. C61 | #8258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462608 | 2 |
| #21461612 | 2 |
| #21461203 | 2 |
| #21461035 | 2 |
| #21460716 | 2 |
| #21460711 | 2 |
| #21444473 | 2 |
| #8258 | 61 |