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. #14543924 | C2 | direct (N × H) |
| 9. #11763175 | C4 | semidirect |
| 12. C2×#10587474 | C4 | semidirect |
| 13. C2×C17×#125 | C4 | semidirect |
| 19. C17×#125 | C2×C4 | semidirect |
| 33. #10587474 | C2×C4 | semidirect |
| 105. C2×#125 | #595 | semidirect |
| 116. C2×C17 | #1412 | semidirect |
| 129. #125 | C2×#595 | semidirect |
| 140. C17 | C2×#1412 | semidirect |
| 211. C2 | #14543924 | 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 |
| #14543924 | 2 |
| C2×#11763175 | 2 |
| C2×#1412 | 17 |