Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#11763238 | C2 | semidirect |
| 2. C2×D16×D17 | C2 | semidirect |
| 3. #14531095 | C2 | direct (N × H) |
| 4. C2×#11762648 | C2 | semidirect |
| 5. C2×#11762647 | C2 | semidirect |
| 6. C2×#11762644 | C2 | semidirect |
| 7. C2×#11762642 | C2 | semidirect |
| 8. C2×C17×D32 | C2 | semidirect |
| 12. #11763238 | C22 | semidirect |
| 13. C2×Dic136 | C22 | semidirect |
| 18. D16×D17 | C22 | semidirect |
| 20. #11762648 | C22 | semidirect |
| 21. #11762647 | C22 | semidirect |
| 22. #11762644 | C22 | semidirect |
| 23. #11762642 | C22 | semidirect |
| 24. C2×#10587465 | C22 | semidirect |
| 26. C2×C17×D16 | C22 | semidirect |
| 27. C17×D32 | C22 | semidirect |
| 28. C2×C17×C32 | C22 | semidirect |
| 45. C17×D16 | C23 | semidirect |
| 51. Dic136 | C23 | semidirect |
| 56. C17×C32 | C23 | semidirect |
| 57. #10587465 | C23 | semidirect |
| 120. C2×D32 | D17 | semidirect |
| 147. C2×D16 | C2×D17 | semidirect |
| 152. D32 | C2×D17 | semidirect |
| 155. C2×C32 | C2×D17 | semidirect |
| 158. C2×C17 | #2263 | semidirect |
| 184. D16 | C22×D17 | semidirect |
| 190. C32 | C22×D17 | semidirect |
| 191. C17 | C2×#2263 | semidirect |
| 265. C2 | #14531095 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763238 | 2 |
| C2×D16×D17 | 2 |
| #14531095 | 2 |
| C2×#11762648 | 2 |
| C2×#11762647 | 2 |
| C2×#11762644 | 2 |
| C2×#11762642 | 2 |
| C2×C17×D32 | 2 |
| C2×#2263 | 17 |