Finite Group DatabasebetaFinite Group Databasebeta← C32×C3⋊((C22⋊C9)⋊C2) #14519208
Order 1944.
772 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C3×C22⋊C9 | C2×C32 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting, socle | C22×C34 | D3 |
| LCS | G ▷ C3×C22⋊C9 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C33×C22⋊C9 | C2 | semidirect |
| 3. C3×C3⋊((C22⋊C9)⋊C2) | C3 | direct (N × H) |
| 11. C32×C22⋊C9 | D3 | semidirect |
| 12. C32×C22⋊C9 | C2×C3 | semidirect |
| 17. C3⋊((C22⋊C9)⋊C2) | C32 | direct (N × H) |
| 25. C22×C33 | D9 | semidirect |
| 38. C3×C22⋊C9 | C3×D3 | semidirect |
| 39. C3×C22⋊C9 | C2×C32 | semidirect |
| 66. C22×C32 | C3×D9 | semidirect |
| 67. C22×C32 | C3⋊D9 | semidirect |
| 78. C22⋊C9 | C32×D3 | semidirect |
| 81. C33 | (C22⋊C9)⋊C2 | semidirect |
| 110. C22×C3 | C32×D9 | semidirect |
| 111. C22×C3 | C3×C3⋊D9 | semidirect |
| 123. C32 | C3×(C22⋊C9)⋊C2 | semidirect |
| 124. C32 | C3⋊((C22⋊C9)⋊C2) | direct (N × H) |
| 139. C22 | C32×C3⋊D9 | semidirect |
| 143. C3 | C32×(C22⋊C9)⋊C2 | semidirect |
| 144. C3 | C3×C3⋊((C22⋊C9)⋊C2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊C9 | 2 |
| C32×#638 | 3 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C32×C3⋊D9 | 4 |