Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1001 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 1001 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 19. C32×H(3,𝔽3) | Q8 | semidirect |
| 50. C34 | Dic6 | semidirect |
| 53. C3×H(3,𝔽3) | Dic6 | semidirect |
| 54. C3×H(3,𝔽3) | Dic6 | semidirect |
| 104. C33 | #627 | semidirect |
| 106. C33 | #634 | semidirect |
| 108. H(3,𝔽3) | #627 | semidirect |
| 159. C32 | #6229 | semidirect |
| 161. C32 | #6293 | semidirect |
| 182. C3 | #10619894 | semidirect |
| 183. C3 | #10619988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C3⋊#1084) | 2 |
| C3×C3⋊#1084 | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C3×#6293 | 3 |
| #10619988 | 3 |
| #10619894 | 3 |