Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
378 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545140 | C2 | semidirect |
| 3. C2×#11763738 | C2 | semidirect |
| 5. #14543865 | C2 | semidirect |
| 6. #14543846 | C2 | semidirect |
| 25. #11762594 | C4 | semidirect |
| 26. #11762593 | C4 | semidirect |
| 27. #11762592 | C4 | semidirect |
| 28. C17×#350 | C4 | semidirect |
| 195. #350 | #595 | semidirect |
| 244. C17 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545446 | 2 |
| #14545140 | 2 |
| C2×#11763738 | 2 |
| #14544671 | 2 |
| #14543865 | 2 |
| #14543846 | 2 |
| D17×#350 | 2 |
| #12927 | 17 |