Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
644 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C23×C32 |
| Frattini | C32 | C22×C32×D3 |
| Fitting | C22×#6909 | C2 |
| hypercenter | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 ◁ C22×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6909 | C2 | semidirect |
| 2. C2×#92281 | C2 | direct (N × H) |
| 3. C22×C3×#272 | C3 | semidirect |
| 5. C22×#4174 | C3 | semidirect |
| 6. C2×#6909 | C22 | semidirect |
| 7. #92281 | C22 | direct (N × H) |
| 9. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 10. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C2×C3×#272 | C2×C3 | semidirect |
| 14. C22×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 15. C2×#4174 | C2×C3 | semidirect |
| 16. #6909 | C23 | semidirect |
| 23. C2×C3×H(3,𝔽3) | C2×D3 | semidirect |
| 24. C2×C3×H(3,𝔽3) | C22×C3 | semidirect |
| 25. C3×#272 | C22×C3 | semidirect |
| 28. C2×AΣL(1,𝔽27) | C22×C3 | semidirect |
| 29. #4174 | C22×C3 | semidirect |
| 32. C22×C33 | C3×D3 | semidirect |
| 48. C3×H(3,𝔽3) | C22×D3 | semidirect |
| 49. C3×H(3,𝔽3) | C23×C3 | semidirect |
| 51. AΣL(1,𝔽27) | C23×C3 | semidirect |
| 61. C2×C33 | C2×C3×D3 | semidirect |
| 95. C33 | C22×C3×D3 | semidirect |
| 163. C22 | #92281 | direct (N × H) |
| 172. C2 | C2×#92281 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6909 | 2 |
| C2×#92281 | 2 |
| C22×C3×#272 | 3 |
| C22×D3×H(3,𝔽3) | 3 |
| C22×#4174 | 3 |