Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D19 | C2 | semidirect |
| 3. #11926837 | C2 | semidirect |
| 4. #11926833 | C2 | semidirect |
| 5. #11926829 | C2 | semidirect |
| 6. #11926825 | C2 | semidirect |
| 7. #11926821 | C2 | semidirect |
| 8. #11926583 | C2 | semidirect |
| 9. #11926566 | C2 | semidirect |
| 11. C19×#475 | C2 | semidirect |
| 46. #64545 | Q8 | semidirect |
| 86. Q8×C19 | C2×Q8 | semidirect |
| 100. D76 | C2×Q8 | semidirect |
| 138. #475 | D19 | semidirect |
| 180. C19 | #3079 | semidirect |
| 226. Q8 | Q8×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D19 | 2 |
| C4×#64545 | 2 |
| #11926837 | 2 |
| #11926833 | 2 |
| #11926829 | 2 |
| #11926825 | 2 |
| #11926821 | 2 |
| #11926583 | 2 |
| #11926566 | 2 |
| #11926544 | 2 |
| C19×#475 | 2 |
| #3079 | 19 |