Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10597364 | C2 | semidirect |
| 2. #11927206 | C2 | semidirect |
| 3. #11926928 | C2 | semidirect |
| 4. #11926791 | C2 | semidirect |
| 5. #11926766 | C2 | semidirect |
| 6. #11926701 | C2 | semidirect |
| 7. #11926692 | C2 | semidirect |
| 8. #11926623 | C2 | semidirect |
| 9. C4×Q16×C19 | C2 | semidirect |
| 50. Q16×C19 | D4 | semidirect |
| 120. C4×Q16 | D19 | semidirect |
| 153. C19 | #3277 | semidirect |
| 170. Q16 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597364 | 2 |
| #11927206 | 2 |
| #11926928 | 2 |
| #11926791 | 2 |
| #11926766 | 2 |
| #11926701 | 2 |
| #11926692 | 2 |
| #11926623 | 2 |
| C4×Q16×C19 | 2 |
| #3277 | 19 |