Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 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 |
|---|---|---|
| 4. #14527336 | C2 | semidirect |
| 5. #14527334 | C2 | semidirect |
| 6. #14526649 | C2 | semidirect |
| 7. C17×#1288 | C2 | semidirect |
| 11. #11763156 | C4 | semidirect |
| 12. #11763156 | C4 | semidirect |
| 42. #10587555 | C2×C4 | semidirect |
| 43. #10587555 | C2×C4 | semidirect |
| 50. C4×C8×C17 | C2×C4 | semidirect |
| 148. #1288 | D17 | semidirect |
| 222. C4×C8 | C4×D17 | semidirect |
| 229. C17 | #9425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539159 | 2 |
| #14531960 | 2 |
| #14527497 | 2 |
| #14527336 | 2 |
| #14527334 | 2 |
| #14526649 | 2 |
| C17×#1288 | 2 |
| #9425 | 17 |