Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11927095 | C2 | semidirect |
| 2. C4×#64545 | C2 | semidirect |
| 3. #11926871 | C2 | semidirect |
| 4. #11926831 | C2 | semidirect |
| 5. #11926744 | C2 | semidirect |
| 6. #11926740 | C2 | semidirect |
| 7. #11926692 | C2 | semidirect |
| 8. #11926629 | C2 | semidirect |
| 9. #11926626 | C2 | semidirect |
| 10. #11926596 | C2 | semidirect |
| 11. C19×#477 | C2 | semidirect |
| 88. Q8×C19 | #41 | semidirect |
| 106. D76 | #41 | semidirect |
| 142. #477 | D19 | semidirect |
| 187. C19 | #3106 | semidirect |
| 233. Q8 | #64545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927095 | 2 |
| C4×#64545 | 2 |
| #11926871 | 2 |
| #11926831 | 2 |
| #11926744 | 2 |
| #11926740 | 2 |
| #11926692 | 2 |
| #11926629 | 2 |
| #11926626 | 2 |
| #11926596 | 2 |
| C19×#477 | 2 |
| #3106 | 19 |