Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #14545839 | C2 | semidirect |
| 4. Q8⋊#63241 | C2 | semidirect |
| 58. Q8×D17 | C16 | semidirect |
| 96. Q8×C17 | C2×C16 | semidirect |
| 116. Dic34 | C2×C16 | semidirect |
| 165. D17 | Q8⋊C16 | semidirect |
| 199. C17 | C2×Q8⋊C16 | semidirect |
| 242. Q8 | #10587665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545970 | 2 |
| C4×#10587665 | 2 |
| #14545839 | 2 |
| Q8⋊#63241 | 2 |
| Q8×#63242 | 2 |
| C2×Q8⋊C16 | 17 |