Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. #21461760 | C2 | semidirect |
| 3. #21461397 | C2 | semidirect |
| 5. #21460705 | C2 | semidirect |
| 6. #21460651 | C2 | semidirect |
| 110. D4×C61 | #108 | semidirect |
| 196. C61 | #8898 | semidirect |
| 281. D4 | #14519848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462747 | 2 |
| #21461760 | 2 |
| #21461397 | 2 |
| #21461155 | 2 |
| #21460705 | 2 |
| #21460651 | 2 |
| #21444198 | 2 |
| #8898 | 61 |