Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. #11926891 | C2 | semidirect |
| 3. #11926744 | C2 | semidirect |
| 5. #11926289 | C2 | semidirect |
| 6. #11926273 | C2 | semidirect |
| 7. C19×Q8⋊C8 | C2 | semidirect |
| 54. Q8×C19 | D8 | semidirect |
| 68. D76 | SD16 | semidirect |
| 100. Q8⋊C8 | D19 | semidirect |
| 124. C19 | #1627 | semidirect |
| 157. Q8 | D152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D76 | 2 |
| #11926891 | 2 |
| #11926744 | 2 |
| #11926740 | 2 |
| #11926289 | 2 |
| #11926273 | 2 |
| C19×Q8⋊C8 | 2 |
| #1627 | 19 |