Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 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×#10587500 | C2 | semidirect |
| 4. #14531053 | C2 | direct (N × H) |
| 5. C2×#11762585 | C2 | semidirect |
| 6. C2×C17×#494 | C2 | semidirect |
| 12. C2×#10587500 | C22 | semidirect |
| 18. #11762585 | C22 | semidirect |
| 23. C17×#494 | C22 | semidirect |
| 123. C2×#494 | D17 | semidirect |
| 153. #494 | C2×D17 | semidirect |
| 156. C2×C17 | #2251 | semidirect |
| 192. C17 | C2×#2251 | semidirect |
| 268. C2 | #14531053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587500 | 2 |
| C22×#10587499 | 2 |
| C2×#11763193 | 2 |
| #14531053 | 2 |
| C2×#11762585 | 2 |
| C2×C17×#494 | 2 |
| C2×#2251 | 17 |