Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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×#10597257 | C2 | semidirect |
| 2. #11926960 | C2 | semidirect |
| 3. #11926820 | C2 | semidirect |
| 5. #11926359 | C2 | semidirect |
| 6. #11926356 | C2 | semidirect |
| 7. C19×#368 | C2 | semidirect |
| 72. #368 | D19 | semidirect |
| 94. C19 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597257 | 2 |
| #11926960 | 2 |
| #11926820 | 2 |
| #11926815 | 2 |
| #11926359 | 2 |
| #11926356 | 2 |
| C19×#368 | 2 |
| #2223 | 19 |