Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 122 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. #21462025 | C2 | semidirect |
| 2. C2×#16840625 | C2 | semidirect |
| 3. #21460775 | C2 | semidirect |
| 4. #21460773 | C2 | semidirect |
| 52. #135×C61 | C8 | semidirect |
| 71. Q16×C61 | C2×C8 | semidirect |
| 74. D8×C61 | C2×C8 | semidirect |
| 174. C61 | #11592 | semidirect |
| 177. #135 | #92420 | semidirect |
| 221. Q16 | C2×#92420 | semidirect |
| 224. D8 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462025 | 2 |
| C2×#16840625 | 2 |
| #21460775 | 2 |
| #21460773 | 2 |
| #135×Dic61 | 2 |
| #11592 | 61 |