Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
657 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
|---|---|---|
| 4. Dic6×3−1+2 | C3 | semidirect |
| 6. C3×C9×Dic6 | C3 | semidirect |
| 19. C3×#737 | Q8 | semidirect |
| 54. #737 | Dic6 | direct (N × H) |
| 55. C3×3−1+2 | C3×Q8 | semidirect |
| 57. C32×C9 | C3×Q8 | semidirect |
| 92. 3−1+2 | C3×Dic6 | semidirect |
| 98. C3×C9 | C3×Dic6 | semidirect |
| 103. Dic6 | #737 | direct (N × H) |
| 141. C3 | Q8×#737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#737 | 2 |
| Dic3×#737 | 2 |
| Q8×#737 | 3 |
| Dic6×3−1+2 | 3 |
| Dic6×H(3,𝔽3) | 3 |
| C3×C9×Dic6 | 3 |