Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #14531509 | C2 | semidirect |
| 3. #14527453 | C2 | semidirect |
| 4. #14527344 | C2 | semidirect |
| 5. #14526644 | C2 | semidirect |
| 6. #14526613 | C2 | semidirect |
| 7. C17×#1963 | C2 | semidirect |
| 10. #11763185 | C4 | semidirect |
| 11. #11763157 | C4 | semidirect |
| 33. C17×C4⋊Q8 | C2×C4 | semidirect |
| 34. C17×#127 | C2×C4 | semidirect |
| 68. C4×#3622 | C2×C4 | semidirect |
| 111. C42×C17 | D8 | semidirect |
| 180. #1963 | D17 | semidirect |
| 245. C4⋊Q8 | C4×D17 | semidirect |
| 250. #127 | C4×D17 | semidirect |
| 280. C17 | #9299 | semidirect |
| 331. C42 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539699 | 2 |
| #14531509 | 2 |
| #14527453 | 2 |
| #14527344 | 2 |
| #14526644 | 2 |
| #14526613 | 2 |
| C17×#1963 | 2 |
| #9299 | 17 |