Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
794 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92333 |
| commutator, cosocle, hypocenter | #732 | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×#6911 | C2 |
| socle | C22×C3 | C3×#272 |
| LCS | G ▷ #732 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6911 | C2 | semidirect |
| 2. C2×#92333 | C2 | direct (N × H) |
| 5. C22×#4185 | C3 | semidirect |
| 6. C2×#6911 | C22 | semidirect |
| 7. #92333 | C22 | direct (N × H) |
| 8. C22×C3×3−1+2 | D3 | semidirect |
| 9. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 14. C22×#732 | C2×C3 | semidirect |
| 15. C2×#4185 | C2×C3 | semidirect |
| 16. #6911 | C23 | semidirect |
| 23. C2×C3×3−1+2 | C2×D3 | semidirect |
| 24. C2×C3×H(3,𝔽3) | C2×D3 | semidirect |
| 29. C2×#732 | C22×C3 | semidirect |
| 30. #4185 | C22×C3 | semidirect |
| 38. C22×H(3,𝔽3) | C3×D3 | semidirect |
| 40. C22×C3×C9 | C3×D3 | semidirect |
| 45. C3×3−1+2 | C22×D3 | semidirect |
| 46. C3×H(3,𝔽3) | C22×D3 | semidirect |
| 49. #732 | C23×C3 | semidirect |
| 63. C2×H(3,𝔽3) | C2×C3×D3 | semidirect |
| 65. C2×C3×C9 | C2×C3×D3 | semidirect |
| 90. H(3,𝔽3) | C22×C3×D3 | semidirect |
| 92. C3×C9 | C22×C3×D3 | semidirect |
| 141. C22 | #92333 | direct (N × H) |
| 148. C2 | C2×#92333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6911 | 2 |
| C2×#92333 | 2 |
| C22×C3×AGL(1,ℤ/9) | 3 |
| C22×C3×(C3⋊D3)⋊C3 | 3 |
| C22×#4185 | 3 |