Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1436 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1436 conjugacy classes of subgroups — too many to draw. Only its 232 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×#10587680 | C2 | semidirect |
| 2. C2×#11763841 | C2 | semidirect |
| 3. #14544762 | C2 | semidirect |
| 4. #14544730 | C2 | semidirect |
| 5. #14544609 | C2 | semidirect |
| 6. #14544522 | C2 | semidirect |
| 42. C2×#63242 | D4 | semidirect |
| 203. C17 | #21444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587680 | 2 |
| C2×#11763841 | 2 |
| #14544762 | 2 |
| #14544730 | 2 |
| #14544609 | 2 |
| #14544522 | 2 |
| #14532001 | 2 |
| #21444 | 17 |