Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
294 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 55 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. #14541917 | C2 | semidirect |
| 2. #14531099 | C2 | semidirect |
| 3. #14531096 | C2 | semidirect |
| 4. #14530888 | C2 | semidirect |
| 5. #14526970 | C2 | semidirect |
| 6. #14526923 | C2 | semidirect |
| 7. C17×#1418 | C2 | semidirect |
| 15. C2×D272 | C22 | semidirect |
| 22. #11762643 | C22 | semidirect |
| 25. C17×M64 | C22 | semidirect |
| 26. C17×#367 | C22 | semidirect |
| 40. C17×Q32 | D4 | semidirect |
| 42. C17×D16 | D4 | semidirect |
| 51. Dic136 | D4 | semidirect |
| 55. D272 | D4 | semidirect |
| 129. #1418 | D17 | semidirect |
| 162. M64 | C2×D17 | semidirect |
| 163. #367 | C2×D17 | semidirect |
| 186. Q32 | D68 | semidirect |
| 195. D16 | D68 | semidirect |
| 204. C17 | #13667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541917 | 2 |
| #14531099 | 2 |
| #14531096 | 2 |
| #14530888 | 2 |
| #14526970 | 2 |
| #14526923 | 2 |
| C17×#1418 | 2 |
| #13667 | 17 |