Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1770 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 312 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. C2×#11763754 | C2 | semidirect |
| 2. C2×C42×#595 | C2 | semidirect |
| 4. #14543963 | C2 | semidirect |
| 12. C2×#10587584 | C4 | semidirect |
| 13. C2×#10587562 | C4 | semidirect |
| 14. C2×#10587565 | C4 | semidirect |
| 20. C2×C17×#126 | C4 | semidirect |
| 77. C42×C17 | C22⋊C4 | semidirect |
| 84. C4×Dic17 | C22⋊C4 | semidirect |
| 103. C2×#595 | #126 | semidirect |
| 144. C2×#126 | #595 | semidirect |
| 190. C17 | #14711 | semidirect |
| 224. C42 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763754 | 2 |
| C2×C42×#595 | 2 |
| #14543965 | 2 |
| #14543963 | 2 |
| C2×#126×D17 | 2 |
| #14711 | 17 |