Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11927267 | C2 | semidirect |
| 2. Q8×D76 | C2 | semidirect |
| 3. #11926904 | C2 | semidirect |
| 4. #11926895 | C2 | semidirect |
| 5. #11926840 | C2 | semidirect |
| 6. #11926825 | C2 | semidirect |
| 8. #11926750 | C2 | semidirect |
| 9. #11926646 | C2 | semidirect |
| 11. C19×#446 | C2 | semidirect |
| 126. #446 | D19 | semidirect |
| 163. C19 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927267 | 2 |
| Q8×D76 | 2 |
| #11926904 | 2 |
| #11926895 | 2 |
| #11926840 | 2 |
| #11926825 | 2 |
| #11926760 | 2 |
| #11926750 | 2 |
| #11926646 | 2 |
| C4×D152 | 2 |
| C19×#446 | 2 |
| #3367 | 19 |