Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. C2×#10597362 | C2 | semidirect |
| 2. #11927214 | C2 | semidirect |
| 3. #11927197 | C2 | semidirect |
| 4. #11926770 | C2 | semidirect |
| 5. #11926751 | C2 | semidirect |
| 6. #11926736 | C2 | semidirect |
| 7. #11926703 | C2 | semidirect |
| 8. #11926688 | C2 | semidirect |
| 9. C4×#64516 | C2 | semidirect |
| 10. C8×D76 | C2 | semidirect |
| 11. C19×#492 | C2 | semidirect |
| 80. #64516 | D4 | semidirect |
| 128. C4×C19 | #135 | semidirect |
| 138. #492 | D19 | semidirect |
| 182. C19 | #3284 | semidirect |
| 272. C4 | #10597362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597362 | 2 |
| #11927214 | 2 |
| #11927197 | 2 |
| #11926770 | 2 |
| #11926751 | 2 |
| #11926736 | 2 |
| #11926703 | 2 |
| #11926688 | 2 |
| C4×#64516 | 2 |
| C8×D76 | 2 |
| C19×#492 | 2 |
| #3284 | 19 |