Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
720 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 720 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. #14539943 | C2 | semidirect |
| 4. #14528447 | C2 | semidirect |
| 5. #14528438 | C2 | semidirect |
| 6. #14528409 | C2 | semidirect |
| 7. #14528387 | C2 | semidirect |
| 8. #14527081 | C2 | semidirect |
| 9. C17×#3185 | C2 | semidirect |
| 12. #11763212 | C22 | semidirect |
| 13. #11763205 | C22 | semidirect |
| 17. #11763161 | C22 | semidirect |
| 18. #11763161 | C22 | semidirect |
| 29. #11762531 | C22 | semidirect |
| 30. #11762530 | C22 | semidirect |
| 31. C8×#3622 | C22 | semidirect |
| 33. C17×#498 | C22 | semidirect |
| 34. C17×#494 | C22 | semidirect |
| 35. C17×#487 | C22 | semidirect |
| 144. #3185 | D17 | semidirect |
| 170. #498 | C2×D17 | semidirect |
| 171. #494 | C2×D17 | semidirect |
| 177. #487 | C2×D17 | semidirect |
| 238. C17 | #19717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539943 | 2 |
| #14539722 | 2 |
| #14539159 | 2 |
| #14528447 | 2 |
| #14528438 | 2 |
| #14528409 | 2 |
| #14528387 | 2 |
| #14527081 | 2 |
| C17×#3185 | 2 |
| #19717 | 17 |