Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
275 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 51 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 | C3⋊(D9⋊A4) |
| commutator, hypocenter | C22×C3×C9 | C2×C9 |
| Frattini | C32 | A4×C3⋊D3 |
| Fitting, cosocle | C22×C32×C9 | C2×C3 |
| socle | C22×C33 | C3×D3 |
| prime radical | C22×C3×C3⋊D9 | C3 |
| LCS | G ▷ C22×C3×C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9⋊(C22⋊C9) | C2 | semidirect |
| 12. C9⋊(C22⋊C9) | D3 | semidirect |
| 15. C22×C3⋊D9 | C9 | semidirect |
| 29. C22×C3×C9 | C2×C9 | semidirect |
| 58. C3⋊D9 | C22⋊C9 | semidirect |
| 75. C22×C9 | D3×C9 | semidirect |
| 89. C3×C9 | C2×C22⋊C9 | semidirect |
| 114. C22×C3 | D9⋊C9 | semidirect |
| 130. C9 | D3×C22⋊C9 | semidirect |
| 145. C22 | C3⋊(D9⋊C9) | semidirect |
| 148. C3 | D9⋊(C22⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊(C22⋊C9) | 2 |
| C22×C3×C3⋊D9 | 3 |
| C3⋊D3×C22⋊C9 | 3 |
| D9⋊(C22⋊C9) | 3 |
| C3⋊(D9⋊C9) | 4 |