Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
544 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D9⋊A4 |
| commutator, cosocle, hypocenter | C22×C9 | C23×C3 |
| Frattini | C3 | C22×D3×A4 |
| Fitting | C24×C9 | C2×C3 |
| socle | C24×C3 | C3×D3 |
| LCS | G ▷ C22×C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C9⋊A4 | C2 | semidirect |
| 2. C2×D9⋊A4 | C2 | direct (N × H) |
| 4. C24×D9 | C3 | semidirect |
| 6. C2×C9⋊A4 | C22 | semidirect |
| 7. D9⋊A4 | C22 | direct (N × H) |
| 10. C24×C9 | C2×C3 | semidirect |
| 14. C23×D9 | C2×C3 | semidirect |
| 18. C9⋊A4 | C23 | semidirect |
| 26. C23×C9 | C22×C3 | semidirect |
| 34. C22×D9 | A4 | semidirect |
| 35. C22×D9 | C22×C3 | semidirect |
| 54. C22×C9 | C2×A4 | semidirect |
| 55. C22×C9 | C23×C3 | semidirect |
| 61. C2×D9 | C2×A4 | semidirect |
| 85. C2×C9 | C22×A4 | semidirect |
| 87. D9 | C22×A4 | semidirect |
| 92. C24 | AGL(1,ℤ/9) | semidirect |
| 110. C9 | C23×A4 | semidirect |
| 122. C23 | C2×AGL(1,ℤ/9) | semidirect |
| 140. C22 | D9⋊A4 | direct (N × H) |
| 141. C22 | C22×AGL(1,ℤ/9) | semidirect |
| 148. C2 | C2×D9⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9⋊A4 | 2 |
| C2×D9⋊A4 | 2 |
| C22×D3×A4 | 3 |
| C24×D9 | 3 |
| C22×AGL(1,ℤ/9) | 4 |