Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
338 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #14530970 | C2 | semidirect |
| 3. #14530962 | C2 | semidirect |
| 4. #14530226 | C2 | semidirect |
| 5. #14526798 | C2 | semidirect |
| 6. #14526709 | C2 | semidirect |
| 7. C17×#1349 | C2 | semidirect |
| 15. C2×#10587489 | C22 | semidirect |
| 22. C22⋊#63214 | C22 | semidirect |
| 25. C17×C22⋊C16 | C22 | semidirect |
| 26. C17×#341 | C22 | semidirect |
| 141. #1349 | D17 | semidirect |
| 180. C22⋊C16 | C2×D17 | semidirect |
| 182. #341 | C2×D17 | semidirect |
| 223. C17 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539644 | 2 |
| #14530970 | 2 |
| #14530962 | 2 |
| #14530226 | 2 |
| #14526798 | 2 |
| #14526709 | 2 |
| C17×#1349 | 2 |
| #12284 | 17 |