Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11927359 | C2 | semidirect |
| 2. #11927358 | C2 | semidirect |
| 3. #11926922 | C2 | semidirect |
| 4. #11926819 | C2 | semidirect |
| 5. #11926817 | C2 | semidirect |
| 6. #11926816 | C2 | semidirect |
| 7. #11926727 | C2 | semidirect |
| 8. #11926725 | C2 | semidirect |
| 9. #11926661 | C2 | semidirect |
| 10. #11926659 | C2 | semidirect |
| 11. C19×#578 | C2 | semidirect |
| 144. #578 | D19 | semidirect |
| 191. C19 | #3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927359 | 2 |
| #11927358 | 2 |
| #11926922 | 2 |
| #11926819 | 2 |
| #11926817 | 2 |
| #11926816 | 2 |
| #11926727 | 2 |
| #11926725 | 2 |
| #11926661 | 2 |
| #11926659 | 2 |
| C19×#578 | 2 |
| #3293 | 19 |