Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 124 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. #21461035 | C2 | semidirect |
| 4. #21461015 | C2 | semidirect |
| 5. #21460651 | C2 | semidirect |
| 6. #21460650 | C2 | semidirect |
| 196. C61 | #8186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519865 | 2 |
| #21461113 | 2 |
| #21461035 | 2 |
| #21461015 | 2 |
| #21460651 | 2 |
| #21460650 | 2 |
| #21444200 | 2 |
| #8186 | 61 |