Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
378 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 112 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. #14545144 | C2 | semidirect |
| 2. C4×#10587529 | C2 | semidirect |
| 3. Q8⋊#63216 | C2 | semidirect |
| 4. #14543735 | C2 | semidirect |
| 57. #63256 | C16 | semidirect |
| 96. Q8×C17 | C2×C16 | semidirect |
| 108. D68 | C2×C16 | semidirect |
| 201. C17 | #11613 | semidirect |
| 242. Q8 | #10587529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545144 | 2 |
| C4×#10587529 | 2 |
| Q8⋊#63216 | 2 |
| #14543735 | 2 |
| C8×#63256 | 2 |
| #11613 | 17 |