Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
514 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14537420 | C2 | semidirect |
| 3. #14527227 | C2 | semidirect |
| 4. #14527116 | C2 | semidirect |
| 5. #14526650 | C2 | semidirect |
| 6. #14526649 | C2 | semidirect |
| 7. C17×#1490 | C2 | semidirect |
| 62. C4×C8×C17 | D4 | semidirect |
| 75. C4×#3622 | D4 | semidirect |
| 188. #1490 | D17 | semidirect |
| 289. C4×C8 | C22⋊D17 | semidirect |
| 296. C17 | #9494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537420 | 2 |
| #14534344 | 2 |
| #14527227 | 2 |
| #14527116 | 2 |
| #14526650 | 2 |
| #14526649 | 2 |
| C17×#1490 | 2 |
| #9494 | 17 |