Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11927078 | C2 | semidirect |
| 2. #11926946 | C2 | semidirect |
| 3. #11926928 | C2 | semidirect |
| 4. #11926899 | C2 | semidirect |
| 5. #11926802 | C2 | semidirect |
| 7. #11926790 | C2 | semidirect |
| 8. #11926657 | C2 | semidirect |
| 9. #11926652 | C2 | semidirect |
| 10. #11926646 | C2 | semidirect |
| 11. C4×M16×C19 | C2 | semidirect |
| 116. C4×M16 | D19 | semidirect |
| 148. C19 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927078 | 2 |
| #11926946 | 2 |
| #11926928 | 2 |
| #11926899 | 2 |
| #11926802 | 2 |
| #11926797 | 2 |
| #11926790 | 2 |
| #11926657 | 2 |
| #11926652 | 2 |
| #11926646 | 2 |
| C4×M16×C19 | 2 |
| #3183 | 19 |