Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
171 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C3⋊S4 |
| commutator, hypocenter | C3×A4 | C2×C27 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C32 | D3×C9 |
| prime radical | C3×C3⋊S4 | C9 |
| cosocle | C3×C9×A4 | C2×C3 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C27 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×C27 | C2 | semidirect |
| 7. C22×C3×C27 | D3 | semidirect |
| 11. A4×C27 | D3 | semidirect |
| 31. C22×C27 | C3⋊D3 | semidirect |
| 38. C3×C27 | S4 | semidirect |
| 39. C3⋊S4 | C27 | direct (N × H) |
| 54. C3×A4 | C2×C27 | semidirect |
| 69. C27 | C3⋊S4 | direct (N × H) |
| 82. C22×C3 | D3×C27 | semidirect |
| 86. A4 | D3×C27 | semidirect |
| 105. C22 | C3⋊D3×C27 | semidirect |
| 110. C3 | S4×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×C27 | 2 |
| C9×C3⋊S4 | 3 |
| S4×C27 | 3 |
| #67×C27 | 3 |
| C3⋊D3×C27 | 4 |