Finite Group DatabasebetaFinite Group Databasebeta← C3⋊(((C22⋊C27)⋊C2)⋊C3) #14518036
Order 1944.
219 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C22⋊C27 | C2×C3 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C32 | C3×D9 |
| LCS | G ▷ C3×C22⋊C27 | |
| UCS | C1 | |
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 |
| 10. #66353 | D3 | semidirect |
| 12. C3×C22⋊C27 | C2×C3 | semidirect |
| 39. C22⋊C27 | C3×D3 | semidirect |
| 109. C22×C3 | D27⋊C3 | semidirect |
| 134. C22 | C3⋊(D27⋊C3) | semidirect |
| 138. C3 | ((C22⋊C27)⋊C2)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66353 | 2 |
| C3×#6233 | 3 |
| C3⋊((C22⋊C27)⋊C2) | 3 |
| ((C22⋊C27)⋊C2)⋊C3 | 3 |
| C3⋊(D27⋊C3) | 4 |