Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 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. #14537036 | C2 | direct (N × H) |
| 2. C2×#11762722 | C2 | semidirect |
| 3. C2×#11762721 | C2 | semidirect |
| 4. C2×#11762720 | C2 | semidirect |
| 6. C2×C17×#393 | C2 | semidirect |
| 8. C23×Dic34 | C22 | semidirect |
| 12. #11762722 | C22 | semidirect |
| 13. #11762721 | C22 | semidirect |
| 14. #11762720 | C22 | semidirect |
| 16. C2×#10587502 | C22 | semidirect |
| 17. C2×#10587502 | C22 | semidirect |
| 18. C23×Q8×C17 | C22 | semidirect |
| 20. C17×#393 | C22 | semidirect |
| 21. C2×C17×#95 | C22 | semidirect |
| 25. C24×D17 | Q8 | semidirect |
| 29. C22×Q8×C17 | C23 | semidirect |
| 35. C22×Dic34 | C23 | semidirect |
| 44. C17×#95 | C23 | semidirect |
| 45. #10587502 | C23 | semidirect |
| 46. #10587502 | C23 | semidirect |
| 60. C23×D17 | C2×Q8 | semidirect |
| 118. C2×#393 | D17 | semidirect |
| 140. C23×Q8 | C2×D17 | semidirect |
| 148. #393 | C2×D17 | semidirect |
| 152. C2×#95 | C2×D17 | semidirect |
| 154. C2×C17 | #2840 | semidirect |
| 169. C22×Q8 | C22×D17 | semidirect |
| 183. #95 | C22×D17 | semidirect |
| 184. C17 | C2×#2840 | semidirect |
| 271. C2 | #14537036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537036 | 2 |
| C2×#11762722 | 2 |
| C2×#11762721 | 2 |
| C2×#11762720 | 2 |
| C2×#11762664 | 2 |
| C2×C17×#393 | 2 |
| C2×#2840 | 17 |