Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #14530928 | C2 | semidirect |
| 3. C8×D136 | C2 | semidirect |
| 4. #14526848 | C2 | semidirect |
| 5. #14526842 | C2 | semidirect |
| 6. #14526830 | C2 | semidirect |
| 7. C17×#1706 | C2 | semidirect |
| 67. D136 | SD16 | semidirect |
| 98. #1706 | D17 | semidirect |
| 159. C17 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530928 | 2 |
| #14530816 | 2 |
| C8×D136 | 2 |
| #14526848 | 2 |
| #14526842 | 2 |
| #14526830 | 2 |
| C17×#1706 | 2 |
| #12418 | 17 |