Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#10597390 | C2 | semidirect |
| 3. #11926937 | C2 | semidirect |
| 4. #11926911 | C2 | semidirect |
| 5. #11926752 | C2 | semidirect |
| 6. #11926748 | C2 | semidirect |
| 7. #11926699 | C2 | semidirect |
| 10. #11926598 | C2 | semidirect |
| 11. C19×#451 | C2 | semidirect |
| 140. #451 | D19 | semidirect |
| 180. C19 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597390 | 2 |
| #11927080 | 2 |
| #11926937 | 2 |
| #11926911 | 2 |
| #11926752 | 2 |
| #11926748 | 2 |
| #11926699 | 2 |
| #11926685 | 2 |
| #11926683 | 2 |
| #11926598 | 2 |
| C19×#451 | 2 |
| #3218 | 19 |