Finite Group DatabasebetaFinite Group DatabasebetaOrder 972.
141 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×A4 |
| commutator, socle, cosocle | C22×C32 | C33 |
| Fitting | C22×C9⋊C9 | C3 |
| prime radical | C32×A4 | C32 |
| hypercenter | C9⋊C9 | A4 |
| hypocenter | C22 | #6894 |
| LCS | G ▷ C22×C32 ▷ C22 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×C9⋊C9 | C3 | semidirect |
| 6. C9⋊(C22⋊C9) | C3 | semidirect |
| 7. (C22⋊C9)⋊C9 | C3 | semidirect |
| 8. (C22⋊C9)⋊C9 | C3 | semidirect |
| 9. (C22⋊C9)⋊C9 | C3 | semidirect |
| 10. (C22⋊C9)⋊C9 | C3 | semidirect |
| 11. (C22⋊C9)⋊C9 | C3 | semidirect |
| 12. (C22⋊C9)⋊C9 | C3 | semidirect |
| 13. (C22⋊C9)⋊C9 | C3 | semidirect |
| 41. C9⋊C9 | A4 | semidirect |
| 64. C22⋊C9 | 3−1+2 | semidirect |
| 111. C22 | #6894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊A4 | 3 |
| C3×C9×A4 | 3 |
| C22×C9⋊C9 | 3 |
| (C3×A4)⋊C9 | 3 |
| C9⋊(C22⋊C9) | 3 |
| (C22⋊C9)⋊C9 | 3 |
| #6894 | 4 |