Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
999 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 999 conjugacy classes of subgroups — too many to draw. Only its 150 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×#6308 | C3 | semidirect |
| 5. #10619956 | C3 | direct (N × H) |
| 20. C32×H(3,𝔽3) | Q8 | semidirect |
| 21. #6308 | C32 | semidirect |
| 68. C34 | Dic6 | semidirect |
| 69. C34 | C3×Q8 | semidirect |
| 73. C3×H(3,𝔽3) | Dic6 | semidirect |
| 74. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 154. C33 | C3×Dic6 | semidirect |
| 155. C33 | C3×Dic6 | semidirect |
| 156. C33 | #634 | semidirect |
| 157. C33 | C32×Q8 | semidirect |
| 161. H(3,𝔽3) | C3×Dic6 | semidirect |
| 227. C32 | #634⋊C3 | semidirect |
| 229. C32 | C32×Dic6 | semidirect |
| 231. C32 | C3×#634 | semidirect |
| 252. C3 | C3×#634⋊C3 | semidirect |
| 253. C3 | #10619956 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×H(3,𝔽3) | 2 |
| C3×C3⋊((C3⋊Dic3)⋊C3) | 2 |
| C3×#6308 | 3 |
| C32×#634 | 3 |
| #10619956 | 3 |
| C3×#634⋊C3 | 3 |