Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545013 | C2 | semidirect |
| 2. #14544470 | C2 | semidirect |
| 3. #14543771 | C2 | semidirect |
| 8. #11763704 | C22 | semidirect |
| 10. #11763683 | C22 | semidirect |
| 11. C22×D136 | C4 | semidirect |
| 16. #11763046 | C4 | semidirect |
| 19. C2×C17×#107 | C4 | semidirect |
| 163. C2×#107 | #595 | semidirect |
| 206. C17 | #11705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545013 | 2 |
| #14544470 | 2 |
| #14543771 | 2 |
| C2×#11763046 | 2 |
| #11705 | 17 |