Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
829 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 829 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 2. C3×C3⋊#1084 | C2 | semidirect |
| 3. H(3,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 8. C3×C3⋊#272 | C4 | semidirect |
| 11. C32×C3⋊Dic3 | D3 | semidirect |
| 15. C3⋊#1084 | D3 | semidirect |
| 21. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 35. C3⋊#272 | Dic3 | semidirect |
| 60. C34 | C4×D3 | semidirect |
| 65. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 66. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 111. C3⋊Dic3 | #272 | semidirect |
| 135. C33 | D3×Dic3 | semidirect |
| 136. C33 | #624 | semidirect |
| 142. H(3,𝔽3) | D3×Dic3 | semidirect |
| 217. C32 | C4×#272 | semidirect |
| 220. C32 | #6294 | semidirect |
| 250. C3 | Dic3×#272 | semidirect |
| 251. C3 | #10619890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#272 | 2 |
| C3×C3⋊#1084 | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C3×#6294 | 3 |
| #10619890 | 3 |
| Dic3×#272 | 3 |