Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1156 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1156 conjugacy classes of subgroups — too many to draw. Only its 130 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. #14544676 | C2 | semidirect |
| 2. C2×#11763661 | C2 | semidirect |
| 3. #14543960 | C2 | semidirect |
| 14. C2×#10587560 | C4 | semidirect |
| 19. C2×#10587579 | C4 | semidirect |
| 21. C2×C17×C4⋊Q8 | C4 | semidirect |
| 215. C2×C4⋊Q8 | #595 | semidirect |
| 277. C17 | #8332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544676 | 2 |
| C2×#11763661 | 2 |
| #14543960 | 2 |
| C2×#11763360 | 2 |
| #8332 | 17 |