Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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. #14537049 | C2 | direct (N × H) |
| 2. C2×#11762745 | C2 | semidirect |
| 3. C2×#11762733 | C2 | semidirect |
| 4. C2×#11762731 | C2 | semidirect |
| 6. C2×C17×#399 | C2 | semidirect |
| 8. C22×C4⋊Dic17 | C22 | semidirect |
| 9. C22×#63225 | C22 | semidirect |
| 13. #11762745 | C22 | semidirect |
| 14. #11762733 | C22 | semidirect |
| 15. #11762731 | C22 | semidirect |
| 17. C2×#10587502 | C22 | semidirect |
| 18. C22×C4⋊C4×C17 | C22 | semidirect |
| 20. C17×#399 | C22 | semidirect |
| 21. C2×C17×#95 | C22 | semidirect |
| 32. C2×C4⋊C4×C17 | C23 | semidirect |
| 42. C2×C4⋊Dic17 | C23 | semidirect |
| 44. C2×#63225 | C23 | semidirect |
| 45. C17×#95 | C23 | semidirect |
| 46. #10587502 | C23 | semidirect |
| 112. C2×#399 | D17 | semidirect |
| 137. C22×C4⋊C4 | C2×D17 | semidirect |
| 143. #399 | C2×D17 | semidirect |
| 148. C2×#95 | C2×D17 | semidirect |
| 150. C2×C17 | #2842 | semidirect |
| 169. C2×C4⋊C4 | C22×D17 | semidirect |
| 179. #95 | C22×D17 | semidirect |
| 180. C17 | C2×#2842 | semidirect |
| 263. C2 | #14537049 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537049 | 2 |
| C2×#11762745 | 2 |
| C2×#11762733 | 2 |
| C2×#11762731 | 2 |
| C2×#11762664 | 2 |
| C2×C17×#399 | 2 |
| C2×#2842 | 17 |