Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
15150 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 15150 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C22×#10587615 | C2 | direct (N × H) |
| 3. C23×#63225 | C2 | semidirect |
| 4. C23×C22⋊Dic17 | C2 | semidirect |
| 5. C23×#63227 | C2 | semidirect |
| 6. C25×C4×C17 | C2 | semidirect |
| 12. C2×#10587615 | C22 | direct (N × H) |
| 13. C22×#63225 | C22 | semidirect |
| 14. C22×C22⋊Dic17 | C22 | semidirect |
| 15. C22×#63227 | C22 | semidirect |
| 19. C24×C4×C17 | C22 | semidirect |
| 30. C23×C4×C17 | C23 | semidirect |
| 37. C2×C22⋊Dic17 | C23 | semidirect |
| 38. #10587615 | C23 | direct (N × H) |
| 39. C2×#63227 | C23 | semidirect |
| 40. C2×#63225 | C23 | semidirect |
| 55. C22×C4×C17 | C24 | semidirect |
| 62. C22⋊Dic17 | C24 | semidirect |
| 63. #63227 | C24 | semidirect |
| 64. #63225 | C24 | semidirect |
| 68. C23×C17 | #123 | semidirect |
| 87. C25×C4 | D17 | semidirect |
| 94. C22×C17 | C2×#123 | semidirect |
| 113. C24×C4 | C2×D17 | semidirect |
| 119. C2×C17 | C22×#123 | semidirect |
| 139. C23×C4 | C22×D17 | semidirect |
| 144. C17 | C23×#123 | semidirect |
| 165. C22×C4 | C23×D17 | semidirect |
| 175. C23 | #10587615 | direct (N × H) |
| 194. C22 | C2×#10587615 | direct (N × H) |
| 204. C2 | C22×#10587615 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C22⋊D17 | 2 |
| C22×#10587615 | 2 |
| C23×#63225 | 2 |
| C23×C22⋊Dic17 | 2 |
| C23×#63227 | 2 |
| C25×C4×C17 | 2 |
| C23×#123 | 17 |