Finite Group DatabasebetaFinite Group Databasebeta← C3×C3⋊((C22⋊C27)⋊C2) #14518035
Order 1944.
231 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 50 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 | C3×C22⋊C27 | C2×C3 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | D9 |
| LCS | G ▷ C3×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 |
| 3. C3⋊((C22⋊C27)⋊C2) | C3 | direct (N × H) |
| 11. C3×C22⋊C27 | D3 | semidirect |
| 12. C3×C22⋊C27 | C2×C3 | semidirect |
| 39. C22⋊C27 | C3×D3 | semidirect |
| 64. C22×C32 | D27 | semidirect |
| 110. C22×C3 | C3×D27 | semidirect |
| 111. C22×C3 | C3⋊D27 | semidirect |
| 120. C32 | (C22⋊C27)⋊C2 | semidirect |
| 137. C22 | C3×C3⋊D27 | semidirect |
| 141. C3 | C3×(C22⋊C27)⋊C2 | semidirect |
| 142. C3 | C3⋊((C22⋊C27)⋊C2) | direct (N × H) |
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 |
| C3×(C22⋊C27)⋊C2 | 3 |
| C3×C3⋊D27 | 4 |