Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 672 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 |
|---|---|---|
| 3. #14530459 | C2 | semidirect |
| 5. #14526914 | C2 | semidirect |
| 6. #14526904 | C2 | semidirect |
| 7. C17×#2123 | C2 | semidirect |
| 9. C2×#10587628 | C4 | semidirect |
| 10. C22×#63230 | C4 | semidirect |
| 18. #11762813 | C4 | semidirect |
| 19. #11762803 | C4 | semidirect |
| 32. C22×Q8×C17 | C2×C4 | semidirect |
| 53. C17×#117 | C2×C4 | semidirect |
| 62. C2×#63223 | C2×C4 | semidirect |
| 63. C22×#3622 | C2×C4 | semidirect |
| 220. #2123 | D17 | semidirect |
| 289. C22×Q8 | C4×D17 | semidirect |
| 316. #117 | C4×D17 | semidirect |
| 335. C17 | #13100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538059 | 2 |
| #14537243 | 2 |
| #14530459 | 2 |
| #14528755 | 2 |
| #14526914 | 2 |
| #14526904 | 2 |
| C17×#2123 | 2 |
| #13100 | 17 |