Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
896 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 195 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. #14539727 | C2 | semidirect |
| 2. #14539704 | C2 | semidirect |
| 3. C2×#11763186 | C2 | semidirect |
| 4. #14539107 | C2 | semidirect |
| 5. #14528450 | C2 | semidirect |
| 6. #14528423 | C2 | semidirect |
| 7. C17×#1452 | C2 | semidirect |
| 14. #11763186 | C22 | semidirect |
| 15. #11763182 | C22 | semidirect |
| 17. #11763160 | C22 | semidirect |
| 18. #11763156 | C22 | semidirect |
| 19. #11763156 | C22 | semidirect |
| 20. #11763156 | C22 | semidirect |
| 28. C17×#322 | C22 | semidirect |
| 132. #1452 | D17 | semidirect |
| 168. #322 | C2×D17 | semidirect |
| 207. C17 | #19698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539727 | 2 |
| #14539704 | 2 |
| C2×#11763186 | 2 |
| #14539107 | 2 |
| #14528450 | 2 |
| #14528423 | 2 |
| C17×#1452 | 2 |
| #19698 | 17 |