Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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. #11927149 | C2 | semidirect |
| 2. #11926943 | C2 | semidirect |
| 3. #11926920 | C2 | semidirect |
| 4. #11926910 | C2 | semidirect |
| 5. #11926908 | C2 | semidirect |
| 6. #11926795 | C2 | semidirect |
| 7. #11926778 | C2 | semidirect |
| 8. #11926654 | C2 | semidirect |
| 9. C4×#64525 | C2 | semidirect |
| 10. #11926500 | C2 | semidirect |
| 11. C19×#540 | C2 | semidirect |
| 111. #540 | D19 | semidirect |
| 153. C19 | #3176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927149 | 2 |
| #11926943 | 2 |
| #11926920 | 2 |
| #11926910 | 2 |
| #11926908 | 2 |
| #11926795 | 2 |
| #11926778 | 2 |
| #11926654 | 2 |
| C4×#64525 | 2 |
| #11926500 | 2 |
| C19×#540 | 2 |
| #3176 | 19 |