Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
770 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 175 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. #14539527 | C2 | semidirect |
| 3. #14539327 | C2 | semidirect |
| 5. #14528462 | C2 | semidirect |
| 6. #14528456 | C2 | semidirect |
| 7. #14528415 | C2 | semidirect |
| 8. #14528407 | C2 | semidirect |
| 9. #14528371 | C2 | semidirect |
| 10. #14527086 | C2 | semidirect |
| 11. C17×#1713 | C2 | semidirect |
| 157. C8×C17 | #137 | semidirect |
| 168. #1713 | D17 | semidirect |
| 265. C17 | #19746 | semidirect |
| 336. C8 | #10587604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539527 | 2 |
| #14539504 | 2 |
| #14539327 | 2 |
| #14539242 | 2 |
| #14528462 | 2 |
| #14528456 | 2 |
| #14528415 | 2 |
| #14528407 | 2 |
| #14528371 | 2 |
| #14527086 | 2 |
| C17×#1713 | 2 |
| #19746 | 17 |