Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11927094 | C2 | semidirect |
| 2. #11927078 | C2 | semidirect |
| 3. #11926928 | C2 | semidirect |
| 4. #11926899 | C2 | semidirect |
| 5. #11926755 | C2 | semidirect |
| 6. #11926750 | C2 | semidirect |
| 7. #11926745 | C2 | semidirect |
| 8. #11926740 | C2 | semidirect |
| 9. #11926708 | C2 | semidirect |
| 10. #11926691 | C2 | semidirect |
| 11. C19×#431 | C2 | semidirect |
| 149. #431 | D19 | semidirect |
| 187. C19 | #3212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927094 | 2 |
| #11927078 | 2 |
| #11926928 | 2 |
| #11926899 | 2 |
| #11926755 | 2 |
| #11926750 | 2 |
| #11926745 | 2 |
| #11926740 | 2 |
| #11926708 | 2 |
| #11926691 | 2 |
| C19×#431 | 2 |
| #3212 | 19 |