Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#11763247 | C2 | semidirect |
| 2. C22×#10587497 | C2 | semidirect |
| 3. #14539265 | C2 | semidirect |
| 4. #14537635 | C2 | semidirect |
| 5. #14530838 | C2 | semidirect |
| 6. #14530818 | C2 | semidirect |
| 7. #14530544 | C2 | semidirect |
| 8. #14530489 | C2 | semidirect |
| 9. C17×#2140 | C2 | semidirect |
| 16. C2×#10587471 | C22 | semidirect |
| 17. C2×D272 | C22 | semidirect |
| 22. #11763192 | C22 | semidirect |
| 23. #11763184 | C22 | semidirect |
| 25. #11762891 | C22 | semidirect |
| 28. #11762627 | C22 | semidirect |
| 29. #11762612 | C22 | semidirect |
| 30. #11762609 | C22 | semidirect |
| 34. C17×#357 | C22 | semidirect |
| 58. C2×D136 | D4 | semidirect |
| 166. #2140 | D17 | semidirect |
| 209. #357 | C2×D17 | semidirect |
| 258. C17 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763247 | 2 |
| C22×#10587497 | 2 |
| #14539265 | 2 |
| #14537635 | 2 |
| #14530838 | 2 |
| #14530818 | 2 |
| #14530544 | 2 |
| #14530489 | 2 |
| C17×#2140 | 2 |
| #33585 | 17 |