Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
390 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 64 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. #14543925 | C2 | direct (N × H) |
| 8. C2×#10587556 | C4 | semidirect |
| 10. #11763174 | C4 | semidirect |
| 13. C2×C17×#97 | C4 | semidirect |
| 27. #10587556 | C2×C4 | semidirect |
| 31. C17×#97 | C2×C4 | semidirect |
| 111. C2×#97 | #595 | semidirect |
| 116. C2×C17 | #1412 | semidirect |
| 139. #97 | C2×#595 | semidirect |
| 140. C17 | C2×#1412 | semidirect |
| 211. C2 | #14543925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763714 | 2 |
| #14543925 | 2 |
| C2×#11763174 | 2 |
| C2×#1412 | 17 |