Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#64528 | C2 | semidirect |
| 3. #11926700 | C2 | direct (N × H) |
| 4. C2×#10597292 | C2 | semidirect |
| 17. C2×#64528 | C22 | semidirect |
| 23. #10597292 | C22 | semidirect |
| 56. C23×C19 | Q16 | semidirect |
| 86. C22×C19 | C2×Q16 | semidirect |
| 102. C2×C19 | #451 | semidirect |
| 124. C19 | C2×#451 | semidirect |
| 156. C23 | #64528 | semidirect |
| 185. C22 | C2×#64528 | semidirect |
| 195. C2 | #11926700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64528 | 2 |
| C2×#10597370 | 2 |
| #11926700 | 2 |
| C2×#10597292 | 2 |
| C2×C22⋊(C19⋊C8) | 2 |
| C23×Q8×C19 | 2 |
| C2×#451 | 19 |