Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #14529572 | C2 | semidirect |
| 5. #14526877 | C2 | semidirect |
| 6. #14526874 | C2 | semidirect |
| 7. C17×#2161 | C2 | semidirect |
| 17. #11762626 | C4 | semidirect |
| 18. #11762623 | C4 | semidirect |
| 126. #2161 | D17 | semidirect |
| 199. C17 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537700 | 2 |
| #14530534 | 2 |
| C2×#11762615 | 2 |
| #14529572 | 2 |
| #14526877 | 2 |
| #14526874 | 2 |
| C17×#2161 | 2 |
| #12942 | 17 |