Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
621 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 621 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 16. C3×AΣL(1,𝔽27) | Q8 | semidirect |
| 48. C34 | Dic6 | semidirect |
| 49. C3×3−1+2 | Dic6 | semidirect |
| 50. C3×H(3,𝔽3) | Dic6 | semidirect |
| 51. AΣL(1,𝔽27) | Dic6 | semidirect |
| 97. C33 | #634 | semidirect |
| 99. 3−1+2 | #634 | semidirect |
| 101. H(3,𝔽3) | #634 | semidirect |
| 154. C3 | #10619660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×AΣL(1,𝔽27) | 2 |
| C3⋊#66330 | 2 |
| C3×#6308 | 3 |
| #10619962 | 3 |
| #10619956 | 3 |
| #10619660 | 3 |