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. #14539939 | C2 | semidirect |
| 3. #14539529 | C2 | semidirect |
| 4. #14528443 | C2 | semidirect |
| 5. #14528434 | C2 | semidirect |
| 6. #14528405 | C2 | semidirect |
| 7. #14528384 | C2 | semidirect |
| 8. #14527081 | C2 | semidirect |
| 11. #11763212 | C22 | semidirect |
| 12. #11763207 | C22 | semidirect |
| 13. #11763205 | C22 | semidirect |
| 14. #11763189 | C22 | semidirect |
| 17. #11763160 | C22 | semidirect |
| 18. #11763159 | C22 | semidirect |
| 19. #11763159 | C22 | semidirect |
| 29. #11762531 | C22 | semidirect |
| 30. #11762530 | C22 | semidirect |
| 31. C8×#3622 | C22 | semidirect |
| 238. C17 | #19717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539939 | 2 |
| #14539725 | 2 |
| #14539529 | 2 |
| #14528443 | 2 |
| #14528434 | 2 |
| #14528405 | 2 |
| #14528384 | 2 |
| #14527081 | 2 |
| C17×#3138 | 2 |
| #19717 | 17 |