Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
362 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 96 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. #14545135 | C2 | semidirect |
| 3. #14543852 | C2 | semidirect |
| 13. C2×#10587483 | C4 | semidirect |
| 14. C2×#10587469 | C4 | semidirect |
| 16. C2×C16×D17 | C4 | semidirect |
| 18. C22×C16×C17 | C4 | semidirect |
| 125. C22×C16 | #595 | semidirect |
| 163. C17 | #12839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545135 | 2 |
| #14544666 | 2 |
| #14543852 | 2 |
| C2×#11763225 | 2 |
| #12839 | 17 |