Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
410 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. #14544996 | C2 | semidirect |
| 4. #14543836 | C2 | semidirect |
| 8. C2×#10587530 | C4 | semidirect |
| 10. C2×#10587538 | C4 | semidirect |
| 11. C2×#10587529 | C4 | semidirect |
| 13. C22×#63216 | C4 | semidirect |
| 22. #11762591 | C4 | semidirect |
| 23. #11762590 | C4 | semidirect |
| 24. C17×#349 | C4 | semidirect |
| 152. #349 | #595 | semidirect |
| 195. C17 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763868 | 2 |
| #14544996 | 2 |
| #14544540 | 2 |
| #14543836 | 2 |
| #14530403 | 2 |
| #12613 | 17 |