Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1354 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 1354 conjugacy classes of subgroups — too many to draw. Only its 368 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. #14544522 | C2 | semidirect |
| 3. #14544510 | C2 | semidirect |
| 7. #11763777 | C4 | semidirect |
| 9. C2×#10587542 | C22 | semidirect |
| 10. #11763675 | C22 | semidirect |
| 29. C2×#63242 | C2×C4 | semidirect |
| 36. #10587543 | C2×C4 | semidirect |
| 88. C22×D17 | #97 | semidirect |
| 178. C17 | #20526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763777 | 2 |
| #14544522 | 2 |
| #14544510 | 2 |
| C2×#11762656 | 2 |
| #20526 | 17 |