Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2190 conjugacy classes of subgroups; only the 1372 normal subgroups are shown.
This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 1372 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. #21462734 | C2 | semidirect |
| 2. #21462712 | C2 | semidirect |
| 3. #41×#92420 | C2 | semidirect |
| 4. C2×Q8×#92420 | C2 | semidirect |
| 34. 2−1+4×C61 | C8 | semidirect |
| 37. #41×C61 | C2×C8 | semidirect |
| 38. C2×Q8×C61 | C2×C8 | semidirect |
| 67. #92420 | 2−1+4 | direct (N × H) |
| 100. C61 | C8×2−1+4 | semidirect |
| 101. 2−1+4 | #92420 | direct (N × H) |
| 119. #41 | C2×#92420 | semidirect |
| 120. C2×Q8 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462734 | 2 |
| #21462712 | 2 |
| #41×#92420 | 2 |
| C2×Q8×#92420 | 2 |
| 2−1+4×Dic61 | 2 |
| C8×2−1+4 | 61 |