Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
183 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 38 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⋊D27 |
| commutator, cosocle, hypocenter | A4×C27 | C2×C3 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C32 | C3⋊D9 |
| LCS | G ▷ A4×C27 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×C27 | C2 | semidirect |
| 3. A4⋊D27 | C3 | direct (N × H) |
| 8. C22×C3×C27 | D3 | semidirect |
| 10. C3×C22⋊C27 | D3 | semidirect |
| 14. A4×C27 | C2×C3 | semidirect |
| 38. C22×C27 | C3×D3 | semidirect |
| 41. C22⋊C27 | C3×D3 | semidirect |
| 49. C3×C27 | S4 | semidirect |
| 68. C3×A4 | D27 | semidirect |
| 87. C27 | C3×S4 | semidirect |
| 101. C22×C3 | C3⋊D27 | semidirect |
| 105. A4 | C3×D27 | semidirect |
| 125. C22 | C3×C3⋊D27 | semidirect |
| 130. C3 | A4⋊D27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×C27 | 2 |
| C3×C9⋊S4 | 3 |
| A4⋊D27 | 3 |
| C3×(C22⋊C27)⋊C2 | 3 |
| C3×#6171 | 3 |
| C3×C3⋊D27 | 4 |