Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #11926917 | C2 | semidirect |
| 3. #11926839 | C2 | semidirect |
| 4. #11926835 | C2 | semidirect |
| 5. #11926287 | C2 | semidirect |
| 6. #11926273 | C2 | semidirect |
| 7. C19×Q8⋊C8 | C2 | semidirect |
| 53. Q8×C19 | SD16 | semidirect |
| 99. Q8⋊C8 | D19 | semidirect |
| 123. C19 | #1631 | semidirect |
| 153. Q8 | #64516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927216 | 2 |
| #11926917 | 2 |
| #11926839 | 2 |
| #11926835 | 2 |
| #11926287 | 2 |
| #11926273 | 2 |
| C19×Q8⋊C8 | 2 |
| #1631 | 19 |