Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #11927076 | C2 | semidirect |
| 2. #11926945 | C2 | semidirect |
| 3. #11926927 | C2 | semidirect |
| 4. #11926897 | C2 | semidirect |
| 5. #11926786 | C2 | semidirect |
| 7. #11926772 | C2 | semidirect |
| 8. C4×Dic76 | C2 | semidirect |
| 9. C4×#64526 | C2 | semidirect |
| 10. C4×C8×D19 | C2 | semidirect |
| 11. C4×D8×C19 | C2 | semidirect |
| 123. C4×D8 | D19 | semidirect |
| 157. C19 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927076 | 2 |
| #11926945 | 2 |
| #11926927 | 2 |
| #11926897 | 2 |
| #11926786 | 2 |
| #11926777 | 2 |
| #11926772 | 2 |
| C4×Dic76 | 2 |
| C4×#64526 | 2 |
| C4×C8×D19 | 2 |
| C4×D8×C19 | 2 |
| #3168 | 19 |