Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
771 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 771 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 6. #10619894 | C3 | direct (N × H) |
| 20. C32×H(3,𝔽3) | Q8 | semidirect |
| 54. C34 | Dic6 | semidirect |
| 59. C3×H(3,𝔽3) | Dic6 | semidirect |
| 60. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 113. C33 | #627 | semidirect |
| 114. C33 | C3×Dic6 | semidirect |
| 120. H(3,𝔽3) | C3×Dic6 | semidirect |
| 171. C32 | #6229 | semidirect |
| 172. C32 | C3×#627 | semidirect |
| 194. C3 | #10619894 | direct (N × H) |
| 195. C3 | C3×#6229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C3⋊#1084 | 2 |
| C32×#1084 | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C32×#627 | 3 |
| C3×#6229 | 3 |
| #10619894 | 3 |