Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
950 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 111 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. #14539699 | C2 | semidirect |
| 2. #14537179 | C2 | semidirect |
| 3. #14527453 | C2 | semidirect |
| 4. #14526617 | C2 | semidirect |
| 5. C17×#1962 | C2 | semidirect |
| 25. C17×C4⋊Q8 | D4 | semidirect |
| 26. C17×#127 | D4 | semidirect |
| 45. C4⋊#3622 | D4 | semidirect |
| 76. C42×C17 | D8 | semidirect |
| 117. #1962 | D17 | semidirect |
| 161. C4⋊Q8 | D68 | semidirect |
| 169. #127 | D68 | semidirect |
| 182. C17 | #10280 | semidirect |
| 214. C42 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539699 | 2 |
| #14537179 | 2 |
| #14527453 | 2 |
| #14526617 | 2 |
| C17×#1962 | 2 |
| #10280 | 17 |