Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3294 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 667 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. #14537048 | C2 | direct (N × H) |
| 2. C2×#11762745 | C2 | semidirect |
| 3. C2×#11762732 | C2 | semidirect |
| 6. C22×C4⋊Dic17 | C22 | semidirect |
| 7. C22×#63225 | C22 | semidirect |
| 11. #11762745 | C22 | semidirect |
| 12. #11762732 | C22 | semidirect |
| 14. C2×#10587502 | C22 | semidirect |
| 38. C2×C4⋊Dic17 | C23 | semidirect |
| 40. C2×#63225 | C23 | semidirect |
| 41. #10587502 | C23 | semidirect |
| 140. C2×C17 | #2842 | semidirect |
| 167. C17 | C2×#2842 | semidirect |
| 247. C2 | #14537048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537048 | 2 |
| C2×#11762745 | 2 |
| C2×#11762732 | 2 |
| C2×#11762665 | 2 |
| C2×C17×#379 | 2 |
| C2×#2842 | 17 |