Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11927198 | C2 | semidirect |
| 2. #11926891 | C2 | semidirect |
| 3. #11926740 | C2 | semidirect |
| 4. #11926739 | C2 | semidirect |
| 5. #11926289 | C2 | semidirect |
| 6. #11926273 | C2 | semidirect |
| 7. C19×D4⋊C8 | C2 | semidirect |
| 55. D4×C19 | D8 | semidirect |
| 105. D4⋊C8 | D19 | semidirect |
| 129. C19 | #1625 | semidirect |
| 170. D4 | D152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927198 | 2 |
| #11926891 | 2 |
| #11926740 | 2 |
| #11926739 | 2 |
| #11926289 | 2 |
| #11926273 | 2 |
| C19×D4⋊C8 | 2 |
| #1625 | 19 |