Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14537807 | C2 | semidirect |
| 3. #14528773 | C2 | semidirect |
| 4. #14527210 | C2 | semidirect |
| 5. #14527208 | C2 | semidirect |
| 6. #14526642 | C2 | semidirect |
| 7. C17×#1286 | C2 | semidirect |
| 57. C4×C8×C17 | D4 | semidirect |
| 67. C4×#3622 | D4 | semidirect |
| 181. #1286 | D17 | semidirect |
| 273. C4×C8 | D68 | semidirect |
| 277. C17 | #9485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537807 | 2 |
| #14533686 | 2 |
| #14528773 | 2 |
| #14527210 | 2 |
| #14527208 | 2 |
| #14526642 | 2 |
| C17×#1286 | 2 |
| #9485 | 17 |