Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
444 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 88 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. #14543757 | C2 | direct (N × H) |
| 11. C22×Dic68 | C4 | semidirect |
| 16. #11763068 | C4 | semidirect |
| 19. C2×C17×#106 | C4 | semidirect |
| 37. C2×Dic68 | C2×C4 | semidirect |
| 52. C17×#106 | C2×C4 | semidirect |
| 174. C2×#106 | #595 | semidirect |
| 182. C2×C17 | #1340 | semidirect |
| 218. #106 | C2×#595 | semidirect |
| 221. C17 | C2×#1340 | semidirect |
| 331. C2 | #14543757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763706 | 2 |
| C2×#11763677 | 2 |
| #14543757 | 2 |
| C2×#11763068 | 2 |
| C2×#1340 | 17 |