Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
308 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 72 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. C22×C3×#733 | C2 | semidirect |
| 2. C2×D3×#733 | C2 | semidirect |
| 3. Dic3×#733 | C2 | semidirect |
| 19. C22×#733 | D3 | semidirect |
| 21. C3×#733 | D4 | semidirect |
| 63. #733 | #67 | direct (N × H) |
| 122. #67 | #733 | direct (N × H) |
| 151. C22×C3 | C2×#733 | semidirect |
| 153. C2×D3 | C2×#733 | semidirect |
| 156. Dic3 | C2×#733 | semidirect |
| 181. C22 | D3×#733 | semidirect |
| 186. C3 | D4×#733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#733 | 2 |
| C2×D3×#733 | 2 |
| Dic3×#733 | 2 |
| #67×3−1+2 | 3 |
| C3×C9×#67 | 3 |
| D4×#733 | 3 |