Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
151 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 151 conjugacy classes of subgroups — too many to draw. Only its 29 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 | C22⋊H(3,𝔽3) | C2×C9 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C3 | C9×C3⋊D3 |
| prime radical | #6258 | C9 |
| cosocle | #66436 | C2×C3 |
| LCS | G ▷ C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C27 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757795 | C2 | semidirect |
| 7. C22×C3×C27 | D3 | semidirect |
| 11. A4×C27 | D3 | semidirect |
| 38. C3×C27 | S4 | semidirect |
| 95. C22 | #92319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757795 | 2 |
| #10620044 | 3 |
| S4×C27 | 3 |
| #67×C27 | 3 |
| #92319 | 4 |