Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
478 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. C2×#11763662 | C2 | semidirect |
| 4. #14544062 | C2 | semidirect |
| 5. #14543667 | C2 | semidirect |
| 6. #14543621 | C2 | semidirect |
| 27. #11763122 | C4 | semidirect |
| 31. #11762964 | C4 | semidirect |
| 32. #11762950 | C4 | semidirect |
| 34. C17×#483 | C4 | semidirect |
| 235. #483 | #595 | semidirect |
| 321. C17 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545659 | 2 |
| #14544171 | 2 |
| C2×#11763662 | 2 |
| #14544062 | 2 |
| #14543667 | 2 |
| #14543621 | 2 |
| #14539570 | 2 |
| #9263 | 17 |