Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
191 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 31 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⋊((C22⋊C27)⋊C2) |
| commutator, cosocle, hypocenter | C32⋊(C22⋊C27) | C2 |
| Frattini | C3×C9 | C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C32 | C3⋊D9 |
| LCS | G ▷ C32⋊(C22⋊C27) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32⋊(C22⋊C27) | C2 | semidirect |
| 8. C3×C22⋊C27 | D3 | semidirect |
| 53. C22×C32 | D27 | semidirect |
| 103. C32 | (C22⋊C27)⋊C2 | semidirect |
| 118. C22 | #92206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32⋊(C22⋊C27) | 2 |
| C3×#6233 | 3 |
| C3×(C22⋊C27)⋊C2 | 3 |
| #92206 | 4 |