Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14543857 | C2 | semidirect |
| 4. #14543851 | C2 | semidirect |
| 17. #11762847 | C4 | semidirect |
| 18. #11762844 | C4 | semidirect |
| 20. #106×D17 | C4 | semidirect |
| 22. C2×C17×#106 | C4 | semidirect |
| 167. C2×#106 | #595 | semidirect |
| 214. C17 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545021 | 2 |
| #14544666 | 2 |
| #14543857 | 2 |
| #14543851 | 2 |
| #14537375 | 2 |
| #12873 | 17 |