Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 72 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. #21462731 | C2 | semidirect |
| 2. #21461345 | C2 | semidirect |
| 5. #21460726 | C2 | semidirect |
| 6. #21460677 | C2 | semidirect |
| 231. C61 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462731 | 2 |
| #21461345 | 2 |
| #21461300 | 2 |
| #21461090 | 2 |
| #21460726 | 2 |
| #21460677 | 2 |
| #21456821 | 2 |
| #9334 | 61 |