Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×#10597279 | C2 | semidirect |
| 3. #11926580 | C2 | semidirect |
| 6. #11926316 | C2 | semidirect |
| 7. C19×#344 | C2 | semidirect |
| 17. #10597353 | C4 | semidirect |
| 18. #10597353 | C4 | semidirect |
| 107. #344 | D19 | semidirect |
| 132. C19 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597353 | 2 |
| C2×#10597279 | 2 |
| #11926580 | 2 |
| #11926562 | 2 |
| #11926560 | 2 |
| #11926316 | 2 |
| C19×#344 | 2 |
| #1814 | 19 |