Finite Group DatabasebetaFinite Group Databasebeta← C3×((C22⋊C27)⋊C2)⋊C3 #14517963
Order 1944.
202 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 40 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 | ((C22⋊C27)⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | C22⋊C27 | C2×C32 |
| Frattini | C9 | C32×S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C32 | C3×D9 |
| LCS | G ▷ C22⋊C27 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66353 | C2 | semidirect |
| 3. C3×(C22⋊C27)⋊C2 | C3 | semidirect |
| 4. ((C22⋊C27)⋊C2)⋊C3 | C3 | direct (N × H) |
| 10. #66353 | C2×C3 | semidirect |
| 12. C3×C22⋊C27 | C2×C3 | semidirect |
| 17. (C22⋊C27)⋊C2 | C32 | semidirect |
| 35. C22⋊C27 | C2×C32 | semidirect |
| 96. C22×C3 | D27⋊C3 | semidirect |
| 119. C22 | C3×D27⋊C3 | semidirect |
| 123. C3 | ((C22⋊C27)⋊C2)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66353 | 2 |
| C32×#611 | 3 |
| C3×(C22⋊C27)⋊C2 | 3 |
| ((C22⋊C27)⋊C2)⋊C3 | 3 |
| C3×D27⋊C3 | 4 |