Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#11762847 | C2 | semidirect |
| 3. #14530993 | C2 | semidirect |
| 4. #14530976 | C2 | semidirect |
| 5. #14530572 | C2 | semidirect |
| 6. #14530497 | C2 | semidirect |
| 7. C17×#2112 | C2 | semidirect |
| 20. #11762637 | C22 | semidirect |
| 21. #11762635 | C22 | semidirect |
| 22. #11762614 | C22 | semidirect |
| 23. #11762611 | C22 | semidirect |
| 129. #2112 | D17 | semidirect |
| 201. C17 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538365 | 2 |
| C2×#11762847 | 2 |
| #14530993 | 2 |
| #14530976 | 2 |
| #14530572 | 2 |
| #14530497 | 2 |
| C17×#2112 | 2 |
| #33647 | 17 |