Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 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. #21462582 | C2 | semidirect |
| 2. #21462139 | C2 | semidirect |
| 3. C2×#16840678 | C2 | semidirect |
| 4. #21461976 | C2 | semidirect |
| 5. #21460891 | C2 | semidirect |
| 6. #21460871 | C2 | semidirect |
| 24. #16840205 | C4 | semidirect |
| 25. #16840202 | C4 | semidirect |
| 27. #16840198 | C4 | semidirect |
| 32. C61×#509 | C4 | semidirect |
| 66. C2×Dic244 | C2×C4 | semidirect |
| 78. #14519717 | C2×C4 | semidirect |
| 82. C2×D8×C61 | C2×C4 | semidirect |
| 85. M32×C61 | C2×C4 | semidirect |
| 232. #509 | #6923 | semidirect |
| 249. C61 | #13030 | semidirect |
| 267. C2×D8 | C2×#6923 | semidirect |
| 290. M32 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462582 | 2 |
| #21462139 | 2 |
| C2×#16840678 | 2 |
| #21461976 | 2 |
| #21460891 | 2 |
| #21460871 | 2 |
| #21458951 | 2 |
| #13030 | 61 |