Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #14539333 | C2 | semidirect |
| 3. #14538602 | C2 | semidirect |
| 4. #14529994 | C2 | semidirect |
| 5. #14529765 | C2 | semidirect |
| 6. #14529625 | C2 | semidirect |
| 7. #14528993 | C2 | semidirect |
| 8. #14528595 | C2 | semidirect |
| 9. C17×#2641 | C2 | semidirect |
| 137. #63223 | #41 | semidirect |
| 180. #2641 | D17 | semidirect |
| 288. C17 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14542658 | 2 |
| #14539333 | 2 |
| #14538602 | 2 |
| #14529994 | 2 |
| #14529765 | 2 |
| #14529625 | 2 |
| #14528993 | 2 |
| #14528595 | 2 |
| C17×#2641 | 2 |
| #25690 | 17 |