Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1556 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C32×C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C23×C32 |
| Frattini | C3 | C22×C32×C3⋊D3 |
| Fitting | C22×H(5,𝔽3) | C2 |
| hypercenter | C22×H(3,𝔽3) | C3⋊D3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 ◁ C22×H(3,𝔽3) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×H(5,𝔽3) | C2 | semidirect |
| 2. C2×#92392 | C2 | direct (N × H) |
| 3. C22×C3×#272 | C3 | semidirect |
| 5. C2×H(5,𝔽3) | C22 | semidirect |
| 6. #92392 | C22 | direct (N × H) |
| 8. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 9. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 10. C2×C3×#272 | C2×C3 | semidirect |
| 12. H(5,𝔽3) | C23 | semidirect |
| 15. C22×#272 | C32 | semidirect |
| 17. C2×C3×H(3,𝔽3) | C2×D3 | semidirect |
| 18. C2×C3×H(3,𝔽3) | C22×C3 | semidirect |
| 19. C3×#272 | C22×C3 | semidirect |
| 22. C22×C33 | C3×D3 | semidirect |
| 30. C2×#272 | C2×C32 | semidirect |
| 32. C3×H(3,𝔽3) | C22×D3 | semidirect |
| 33. C3×H(3,𝔽3) | C23×C3 | semidirect |
| 38. C2×C33 | C2×C3×D3 | semidirect |
| 46. #272 | C22×C32 | semidirect |
| 56. C33 | C22×C3×D3 | semidirect |
| 94. C22 | #92392 | direct (N × H) |
| 100. C2 | C2×#92392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×H(5,𝔽3) | 2 |
| C2×#92392 | 2 |
| C22×C3×#272 | 3 |
| C22×D3×H(3,𝔽3) | 3 |