Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
786 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 296 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. #21461872 | C2 | semidirect |
| 3. #21461746 | C2 | semidirect |
| 4. C4⋊C4×#92420 | C2 | semidirect |
| 6. C42×#92420 | C2 | semidirect |
| 45. #126×C61 | C8 | semidirect |
| 67. C4⋊C4×C61 | C2×C8 | semidirect |
| 69. C42×C61 | C2×C8 | semidirect |
| 101. #92420 | #126 | direct (N × H) |
| 144. C61 | C8×#126 | semidirect |
| 151. #126 | #92420 | direct (N × H) |
| 188. C4⋊C4 | C2×#92420 | semidirect |
| 196. C42 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461888 | 2 |
| #21461872 | 2 |
| #21461746 | 2 |
| C4⋊C4×#92420 | 2 |
| C22⋊C4×#92420 | 2 |
| C42×#92420 | 2 |
| #126×Dic61 | 2 |
| C8×#126 | 61 |