Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 179 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. #14539502 | C2 | semidirect |
| 3. #14539178 | C2 | semidirect |
| 4. #14539165 | C2 | semidirect |
| 5. #14528437 | C2 | semidirect |
| 6. #14528430 | C2 | semidirect |
| 7. #14528423 | C2 | semidirect |
| 8. #14528396 | C2 | semidirect |
| 9. C17×#1455 | C2 | semidirect |
| 150. #1455 | D17 | semidirect |
| 237. C17 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539522 | 2 |
| #14539502 | 2 |
| #14539178 | 2 |
| #14539165 | 2 |
| #14528437 | 2 |
| #14528430 | 2 |
| #14528423 | 2 |
| #14528396 | 2 |
| C17×#1455 | 2 |
| #19754 | 17 |