Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
390 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 43 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⋊D9 |
| commutator, Fitting, cosocle, hypocenter | C22×C32⋊C9 | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C22×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×C32⋊C9 | C2 | semidirect |
| 4. C22×#4181 | C3 | semidirect |
| 7. C3×C9×A4 | D3 | semidirect |
| 8. C22×C32⋊C9 | C2×C3 | semidirect |
| 24. #4181 | A4 | direct (N × H) |
| 32. C32×A4 | D9 | semidirect |
| 34. C22×C3×C9 | C3×D3 | semidirect |
| 43. C32⋊C9 | C2×A4 | semidirect |
| 63. C22×C32 | C3×D9 | semidirect |
| 93. C3×C9 | D3×A4 | semidirect |
| 126. A4 | #4181 | direct (N × H) |
| 138. C32 | A4×D9 | semidirect |
| 156. C22 | C3×#4181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×C32⋊C9 | 2 |
| C3×A4×C3⋊D3 | 3 |
| C3×A4×D9 | 3 |
| C22×#4181 | 3 |
| C3×#4181 | 4 |