Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #14530573 | C2 | semidirect |
| 3. C2×#11762637 | C2 | semidirect |
| 6. #14526894 | C2 | semidirect |
| 7. C17×#1382 | C2 | semidirect |
| 21. #11762592 | C4 | semidirect |
| 46. C2×C16×C17 | C2×C4 | semidirect |
| 59. #10587483 | C2×C4 | semidirect |
| 141. #1382 | D17 | semidirect |
| 206. C2×C16 | C4×D17 | semidirect |
| 220. C17 | #12926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537381 | 2 |
| #14530573 | 2 |
| C2×#11762637 | 2 |
| C2×#11762592 | 2 |
| #14528845 | 2 |
| #14526894 | 2 |
| C17×#1382 | 2 |
| #12926 | 17 |