Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 3. #21461301 | C2 | semidirect |
| 4. #21461092 | C2 | semidirect |
| 5. #21460726 | C2 | semidirect |
| 6. #21460677 | C2 | semidirect |
| 233. C61 | #9335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462703 | 2 |
| #21461343 | 2 |
| #21461301 | 2 |
| #21461092 | 2 |
| #21460726 | 2 |
| #21460677 | 2 |
| #21457008 | 2 |
| #9335 | 61 |