Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
230 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 78 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. #21461412 | C2 | semidirect |
| 3. #21460844 | C2 | semidirect |
| 4. #21460779 | C2 | semidirect |
| 6. #21460735 | C2 | semidirect |
| 42. SD32×C61 | C8 | semidirect |
| 53. Q16×C61 | C2×C8 | semidirect |
| 65. C16×C61 | C2×C8 | semidirect |
| 125. C61 | #12065 | semidirect |
| 131. SD32 | #92420 | semidirect |
| 151. Q16 | C2×#92420 | semidirect |
| 169. C16 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461415 | 2 |
| #21461412 | 2 |
| #21460844 | 2 |
| #21460779 | 2 |
| #21460777 | 2 |
| #21460735 | 2 |
| #21447684 | 2 |
| #12065 | 61 |