Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
994 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 175 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. #14539523 | C2 | semidirect |
| 2. #14539231 | C2 | semidirect |
| 3. #14528448 | C2 | semidirect |
| 4. #14528413 | C2 | semidirect |
| 5. #14528399 | C2 | semidirect |
| 6. #14527086 | C2 | semidirect |
| 7. C17×#1705 | C2 | semidirect |
| 13. #11763186 | C22 | semidirect |
| 16. #11763157 | C22 | semidirect |
| 20. #11762530 | C22 | semidirect |
| 21. C17×#498 | C22 | semidirect |
| 23. C82×C17 | C22 | semidirect |
| 89. C8×C17 | AGL(1,ℤ/8) | semidirect |
| 96. #1705 | D17 | semidirect |
| 111. #498 | C2×D17 | semidirect |
| 123. C82 | C2×D17 | semidirect |
| 152. C17 | #19745 | semidirect |
| 195. C8 | #10587600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539523 | 2 |
| #14539231 | 2 |
| #14528448 | 2 |
| #14528413 | 2 |
| #14528399 | 2 |
| #14527086 | 2 |
| C17×#1705 | 2 |
| #19745 | 17 |