Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #11927081 | C2 | semidirect |
| 2. #11926945 | C2 | semidirect |
| 3. #11926929 | C2 | semidirect |
| 4. #11926900 | C2 | semidirect |
| 5. #11926782 | C2 | semidirect |
| 7. #11926776 | C2 | semidirect |
| 8. C4×#64527 | C2 | semidirect |
| 9. C4×D152 | C2 | semidirect |
| 10. C4×C8×D19 | C2 | semidirect |
| 11. C4×Q16×C19 | C2 | semidirect |
| 121. C4×Q16 | D19 | semidirect |
| 157. C19 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927081 | 2 |
| #11926945 | 2 |
| #11926929 | 2 |
| #11926900 | 2 |
| #11926782 | 2 |
| #11926781 | 2 |
| #11926776 | 2 |
| C4×#64527 | 2 |
| C4×D152 | 2 |
| C4×C8×D19 | 2 |
| C4×Q16×C19 | 2 |
| #3168 | 19 |