Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14545987 | C2 | semidirect |
| 2. C4×#10587666 | C2 | semidirect |
| 3. Q8⋊#63241 | C2 | semidirect |
| 4. #14545827 | C2 | semidirect |
| 96. Q8×C17 | M32 | semidirect |
| 108. D68 | M32 | semidirect |
| 201. C17 | #11615 | semidirect |
| 242. Q8 | #10587666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545987 | 2 |
| C4×#10587666 | 2 |
| Q8⋊#63241 | 2 |
| #14545827 | 2 |
| #14545590 | 2 |
| #11615 | 17 |