Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
7034 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 7034 conjugacy classes of subgroups — too many to draw. Only its 675 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. C25×Dic17 | C2 | semidirect |
| 3. C2×#11762686 | C2 | semidirect |
| 4. #14527006 | C2 | semidirect |
| 5. C2×C17×#379 | C2 | semidirect |
| 12. C2×#10587639 | C4 | semidirect |
| 14. C22×#63227 | C22 | semidirect |
| 16. C2×#10587502 | C22 | semidirect |
| 32. C22×C22⋊D17 | C2×C4 | semidirect |
| 38. C23×Dic17 | D4 | semidirect |
| 47. C2×C22⋊Dic17 | C2×C4 | semidirect |
| 58. C24×C17 | C22⋊C4 | semidirect |
| 69. C23×D17 | C22×C4 | semidirect |
| 89. C22×Dic17 | C22×C4 | semidirect |
| 136. C2×Dic17 | #120 | semidirect |
| 140. C2×#379 | D17 | semidirect |
| 149. C22×C17 | #386 | semidirect |
| 216. C17 | #14694 | semidirect |
| 230. C24 | #63227 | semidirect |
| 315. C22 | #11762686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic17 | 2 |
| C22×#10587639 | 2 |
| C2×#11762686 | 2 |
| #14527006 | 2 |
| C2×C17×#379 | 2 |
| #14694 | 17 |