Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. C3×#6229 | C3 | semidirect |
| 5. #10619607 | C3 | semidirect |
| 15. #6909 | Q8 | semidirect |
| 44. C3×H(3,𝔽3) | Dic6 | semidirect |
| 45. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 47. AΣL(1,𝔽27) | C3×Q8 | semidirect |
| 86. C33 | C3×Dic6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6909 | 2 |
| #11757585 | 2 |
| C3×#6229 | 3 |
| Dic6×H(3,𝔽3) | 3 |
| #10619607 | 3 |