Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
484 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | A4×C3⋊D3 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Frattini | C3 | C3×A4×C3⋊D3 |
| Fitting | C22×#737 | C2×C3 |
| socle | C22×C3 | C32×C3⋊D3 |
| prime radical | A4×#272 | C3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#737 | C2 | semidirect |
| 2. C22×#4208 | C3 | semidirect |
| 4. #10620072 | C3 | semidirect |
| 7. C22×#737 | C2×C3 | semidirect |
| 13. #66437 | C2×C3 | semidirect |
| 15. C3×C9×A4 | D3 | semidirect |
| 25. #4208 | A4 | direct (N × H) |
| 31. C22×C3×C9 | C3×D3 | semidirect |
| 38. C3×C22⋊C9 | C3×D3 | semidirect |
| 47. #737 | C2×A4 | semidirect |
| 89. C3×C9 | D3×A4 | semidirect |
| 110. A4 | #4208 | direct (N × H) |
| 129. C22 | C3×#4208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#737 | 2 |
| C22×#4208 | 3 |
| A4×#272 | 3 |
| #10620072 | 3 |
| D3×C9×A4 | 3 |
| C3×#4208 | 4 |