Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
158 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | A42 |
| commutator | C24×C3 | C3×C9 |
| Fitting, socle, prime radical, cosocle | C24×C32 | C32 |
| hypocenter | C24 | C9⋊C9 |
| LCS | G ▷ C24×C3 ▷ C24 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C22×C22⋊C9 | C9 | semidirect |
| 42. C22⋊C9 | C22⋊C9 | semidirect |
| 60. C24 | C9⋊C9 | semidirect |
| 100. C22 | (C22⋊C9)⋊C9 | semidirect |
| 101. C22 | C9⋊(C22⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊(C22⋊C9) | 3 |
| C22×C3×C22⋊C9 | 3 |
| C9⋊(C22⋊C9) | 4 |
| (C22⋊C9)⋊C9 | 4 |