Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
720 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 138 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. #14544570 | C2 | semidirect |
| 2. C4×#10587544 | C2 | semidirect |
| 3. C2×D4⋊#3624 | C2 | semidirect |
| 49. C4⋊#3624 | D4 | semidirect |
| 221. C17 | #9678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544570 | 2 |
| C4×#10587544 | 2 |
| C2×D4⋊#3624 | 2 |
| #127×Dic17 | 2 |
| #9678 | 17 |