Finite Group DatabasebetaFinite Group Databasebeta← C2×C3⋊(C3⋊((C22⋊C9)⋊C2)) #13049288
Order 1296.
864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊((C22⋊C9)⋊C2)) |
| commutator, cosocle, hypocenter | C32×C22⋊C9 | C22 |
| Frattini | C3 | C2×C3⋊(C3⋊S4) |
| Fitting, socle | C23×C33 | D3 |
| LCS | G ▷ C32×C22⋊C9 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×C22⋊C9 | C2 | semidirect |
| 2. C3⋊(C3⋊((C22⋊C9)⋊C2)) | C2 | direct (N × H) |
| 6. C32×C22⋊C9 | C22 | semidirect |
| 12. C2×C3×C22⋊C9 | D3 | semidirect |
| 27. C3×C22⋊C9 | C2×D3 | semidirect |
| 29. C23×C32 | D9 | semidirect |
| 39. C2×C22⋊C9 | C3⋊D3 | semidirect |
| 53. C22×C32 | C2×D9 | semidirect |
| 64. C22⋊C9 | C2×C3⋊D3 | semidirect |
| 67. C23×C3 | C3⋊D9 | semidirect |
| 81. C2×C32 | (C22⋊C9)⋊C2 | semidirect |
| 92. C22×C3 | C2×C3⋊D9 | semidirect |
| 102. C32 | C2×(C22⋊C9)⋊C2 | semidirect |
| 106. C23 | C3⋊(C3⋊D9) | semidirect |
| 114. C2×C3 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 123. C22 | C2×C3⋊(C3⋊D9) | semidirect |
| 125. C3 | C2×C3⋊((C22⋊C9)⋊C2) | semidirect |
| 130. C2 | 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 |
|---|---|
| C2×C32×C22⋊C9 | 2 |
| C3⋊(C3⋊((C22⋊C9)⋊C2)) | 2 |
| C2×#6312 | 3 |
| C2×C3⋊((C22⋊C9)⋊C2) | 3 |
| C2×C3⋊(C3⋊D9) | 4 |