Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
223 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×#732 | C2×C3 |
| socle | C22×C3 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#732 | C2 | semidirect |
| 2. A4×#272 | C3 | semidirect |
| 4. C22×#4178 | C3 | semidirect |
| 5. #10619771 | C3 | semidirect |
| 9. C3×C9×A4 | D3 | semidirect |
| 10. C22×#732 | C2×C3 | semidirect |
| 14. #66362 | C2×C3 | semidirect |
| 19. C22×#272 | C32 | semidirect |
| 28. #4178 | A4 | direct (N × H) |
| 34. C22×C3×C9 | C3×D3 | semidirect |
| 43. C3×C22⋊C9 | C3×D3 | semidirect |
| 52. #732 | C2×A4 | semidirect |
| 67. #272 | C3×A4 | semidirect |
| 101. C3×C9 | D3×A4 | semidirect |
| 133. A4 | #4178 | direct (N × H) |
| 160. C22 | C3×#4178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#732 | 2 |
| A4×#272 | 3 |
| D3×C9×A4 | 3 |
| C22×#4178 | 3 |
| #10619771 | 3 |
| C3×#4178 | 4 |