Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
238 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 82 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. Q16×#92420 | C2 | semidirect |
| 3. #21460850 | C2 | semidirect |
| 4. #21460775 | C2 | semidirect |
| 6. #21460730 | C2 | semidirect |
| 42. SD32×C61 | C8 | semidirect |
| 54. Q16×C61 | C2×C8 | semidirect |
| 66. C16×C61 | C2×C8 | semidirect |
| 128. C61 | #12043 | semidirect |
| 134. SD32 | #92420 | semidirect |
| 154. Q16 | C2×#92420 | semidirect |
| 173. C16 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#92420 | 2 |
| D8×#92420 | 2 |
| #21460850 | 2 |
| #21460775 | 2 |
| #21460773 | 2 |
| #21460730 | 2 |
| SD32×Dic61 | 2 |
| #12043 | 61 |