Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
820 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 171 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. #14540011 | C2 | semidirect |
| 2. #14539166 | C2 | semidirect |
| 3. #14528118 | C2 | semidirect |
| 4. #14528112 | C2 | semidirect |
| 5. #14528107 | C2 | semidirect |
| 6. #14527422 | C2 | semidirect |
| 7. #14527391 | C2 | semidirect |
| 300. C17 | #19005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540011 | 2 |
| #14539166 | 2 |
| #14528118 | 2 |
| #14528112 | 2 |
| #14528107 | 2 |
| #14527422 | 2 |
| #14527391 | 2 |
| C17×#3531 | 2 |
| #19005 | 17 |