Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1088 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×Q8⋊#3633 | C2 | semidirect |
| 27. C22×Q8×C17 | C8 | semidirect |
| 32. C2×Q8×D17 | C8 | semidirect |
| 37. C22×Dic34 | C8 | semidirect |
| 161. Q8×C17 | C22⋊C8 | semidirect |
| 186. Dic34 | C22⋊C8 | semidirect |
| 193. C22×C17 | Q8⋊C8 | semidirect |
| 201. C2×D17 | Q8⋊C8 | semidirect |
| 254. C22×Q8 | #3633 | semidirect |
| 286. C17 | #8311 | semidirect |
| 369. Q8 | C22⋊#3633 | semidirect |
| 426. C22 | Q8⋊#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545924 | 2 |
| C4×C22⋊#3633 | 2 |
| C2×Q8⋊#3633 | 2 |
| C22×Q8×#595 | 2 |
| #8311 | 17 |