Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1506 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 180 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. C22×#10587548 | C2 | semidirect |
| 2. #14544448 | C2 | semidirect |
| 3. C4×(C2×#595)⋊C4 | C2 | semidirect |
| 14. C2×#10587555 | C4 | semidirect |
| 15. C2×#10587622 | C4 | semidirect |
| 19. C2×C17×#127 | C4 | semidirect |
| 38. C2×C4×#595 | D4 | semidirect |
| 42. C2×#63243 | D4 | semidirect |
| 139. C2×C4×C17 | #104 | semidirect |
| 197. C2×#127 | #595 | semidirect |
| 253. C17 | #11011 | semidirect |
| 356. C2×C4 | #10587548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587548 | 2 |
| #14544448 | 2 |
| C4×(C2×#595)⋊C4 | 2 |
| C2×#11763357 | 2 |
| #11011 | 17 |