Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #14539362 | C2 | semidirect |
| 2. #14539361 | C2 | semidirect |
| 3. #14539211 | C2 | semidirect |
| 4. #14539207 | C2 | semidirect |
| 5. #14528457 | C2 | semidirect |
| 6. #14528455 | C2 | semidirect |
| 7. #14528453 | C2 | semidirect |
| 8. #14528451 | C2 | semidirect |
| 9. #14528449 | C2 | semidirect |
| 10. D17×#322 | C2 | semidirect |
| 11. C17×#1721 | C2 | semidirect |
| 135. C8×D17 | D8 | semidirect |
| 179. #1721 | D17 | semidirect |
| 281. C17 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539362 | 2 |
| #14539361 | 2 |
| #14539211 | 2 |
| #14539207 | 2 |
| #14528457 | 2 |
| #14528455 | 2 |
| #14528453 | 2 |
| #14528451 | 2 |
| #14528449 | 2 |
| D17×#322 | 2 |
| C17×#1721 | 2 |
| #19616 | 17 |