Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
396 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 72 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. #14545021 | C2 | semidirect |
| 2. #14544666 | C2 | semidirect |
| 3. #14543754 | C2 | semidirect |
| 8. #11763706 | C22 | semidirect |
| 10. #11763677 | C22 | semidirect |
| 13. #11763059 | C4 | semidirect |
| 17. #11762847 | C4 | semidirect |
| 19. C22×D8×C17 | C4 | semidirect |
| 149. C22×D8 | #595 | semidirect |
| 203. C17 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545021 | 2 |
| #14544666 | 2 |
| #14543754 | 2 |
| #14538428 | 2 |
| #11868 | 17 |