Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11927099 | C2 | semidirect |
| 3. #11926936 | C2 | semidirect |
| 4. #11926904 | C2 | semidirect |
| 5. #11926903 | C2 | semidirect |
| 6. #11926752 | C2 | semidirect |
| 7. #11926742 | C2 | semidirect |
| 8. #11926705 | C2 | semidirect |
| 9. #11926703 | C2 | semidirect |
| 10. #11926599 | C2 | semidirect |
| 11. C19×#497 | C2 | semidirect |
| 139. #497 | D19 | semidirect |
| 184. C19 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927099 | 2 |
| #11927093 | 2 |
| #11926936 | 2 |
| #11926904 | 2 |
| #11926903 | 2 |
| #11926752 | 2 |
| #11926742 | 2 |
| #11926705 | 2 |
| #11926703 | 2 |
| #11926599 | 2 |
| C19×#497 | 2 |
| #3216 | 19 |