Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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. Q8×D76 | C2 | semidirect |
| 2. #11926903 | C2 | semidirect |
| 3. #11926890 | C2 | semidirect |
| 4. #11926834 | C2 | semidirect |
| 5. #11926829 | C2 | semidirect |
| 6. #11926756 | C2 | semidirect |
| 8. #11926675 | C2 | semidirect |
| 9. #11926654 | C2 | semidirect |
| 10. C4×#64527 | C2 | semidirect |
| 11. C19×#559 | C2 | semidirect |
| 120. #559 | D19 | semidirect |
| 165. C19 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D76 | 2 |
| #11926903 | 2 |
| #11926890 | 2 |
| #11926834 | 2 |
| #11926829 | 2 |
| #11926756 | 2 |
| #11926736 | 2 |
| #11926675 | 2 |
| #11926654 | 2 |
| C4×#64527 | 2 |
| C19×#559 | 2 |
| #3373 | 19 |