Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14530393 | C2 | semidirect |
| 3. #14528821 | C2 | semidirect |
| 4. #14526800 | C2 | semidirect |
| 5. #14526799 | C2 | semidirect |
| 6. #14526798 | C2 | semidirect |
| 7. C17×#1349 | C2 | semidirect |
| 21. C22⋊#63214 | C22 | semidirect |
| 23. #11762574 | C22 | semidirect |
| 25. C17×C22⋊C16 | C22 | semidirect |
| 26. C17×#341 | C22 | semidirect |
| 162. #1349 | D17 | semidirect |
| 204. C22⋊C16 | C2×D17 | semidirect |
| 206. #341 | C2×D17 | semidirect |
| 252. C17 | #11895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17×#466 | 2 |
| #14530393 | 2 |
| #14528821 | 2 |
| #14526800 | 2 |
| #14526799 | 2 |
| #14526798 | 2 |
| C17×#1349 | 2 |
| #11895 | 17 |