Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 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. #11927101 | C2 | semidirect |
| 3. #11926953 | C2 | semidirect |
| 4. #11926938 | C2 | semidirect |
| 5. #11926913 | C2 | semidirect |
| 6. #11926904 | C2 | semidirect |
| 7. #11926802 | C2 | semidirect |
| 9. C4×Dic76 | C2 | semidirect |
| 10. C4×#64516 | C2 | semidirect |
| 11. C4×M16×C19 | C2 | semidirect |
| 135. C4×M16 | D19 | semidirect |
| 172. C19 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927101 | 2 |
| #11927078 | 2 |
| #11926953 | 2 |
| #11926938 | 2 |
| #11926913 | 2 |
| #11926904 | 2 |
| #11926802 | 2 |
| #11926790 | 2 |
| C4×Dic76 | 2 |
| C4×#64516 | 2 |
| C4×M16×C19 | 2 |
| #3172 | 19 |