Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
778 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 778 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 |
|---|---|---|
| 2. #14545785 | C2 | direct (N × H) |
| 20. C22×Q8×C17 | C8 | semidirect |
| 25. C2×Q8×D17 | C8 | semidirect |
| 30. C22×Dic34 | C8 | semidirect |
| 56. C2×Q8×C17 | C2×C8 | semidirect |
| 82. C2×Dic34 | C2×C8 | semidirect |
| 169. C2×C17 | #1272 | semidirect |
| 172. D17 | #1272 | semidirect |
| 184. C22×Q8 | #3633 | semidirect |
| 202. C17 | C2×#1272 | semidirect |
| 218. C2×Q8 | C2×#3633 | semidirect |
| 322. C2 | #14545785 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×#3633)⋊C4 | 2 |
| #14545785 | 2 |
| C2×(C2×#595)⋊Q8 | 2 |
| C2×#1272 | 17 |