Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #11926553 | C2 | semidirect |
| 4. #11926451 | C2 | semidirect |
| 5. #11926312 | C2 | semidirect |
| 6. #11926305 | C2 | semidirect |
| 11. C19×#137 | C4 | semidirect |
| 37. C2×Q8×C19 | C2×C4 | semidirect |
| 50. M16×C19 | C2×C4 | semidirect |
| 135. #137 | Dic19 | semidirect |
| 152. C19 | #1882 | semidirect |
| 162. C2×Q8 | C2×Dic19 | semidirect |
| 177. M16 | C2×Dic19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927027 | 2 |
| C2×#10597294 | 2 |
| #11926553 | 2 |
| #11926451 | 2 |
| #11926312 | 2 |
| #11926305 | 2 |
| C2×C19×#137 | 2 |
| #1882 | 19 |