Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #11927024 | C2 | semidirect |
| 3. #11926883 | C2 | semidirect |
| 4. #11926873 | C2 | semidirect |
| 5. #11926867 | C2 | semidirect |
| 6. #11926861 | C2 | semidirect |
| 7. #11926587 | C2 | semidirect |
| 8. C2×#10597274 | C2 | semidirect |
| 9. #11926545 | C2 | semidirect |
| 10. #11926510 | C2 | semidirect |
| 11. C19×#416 | C2 | semidirect |
| 137. #416 | D19 | semidirect |
| 174. C19 | #3099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927122 | 2 |
| #11927024 | 2 |
| #11926883 | 2 |
| #11926873 | 2 |
| #11926867 | 2 |
| #11926861 | 2 |
| #11926587 | 2 |
| C2×#10597274 | 2 |
| #11926545 | 2 |
| #11926510 | 2 |
| C19×#416 | 2 |
| #3099 | 19 |