Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
646 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 84 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 | C9⋊S4 |
| commutator, cosocle, hypocenter | C9×A4 | C2×C32 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C9×A4 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C9×A4 | C2 | semidirect |
| 3. C3×C9⋊S4 | C3 | direct (N × H) |
| 8. C22×C32×C9 | D3 | semidirect |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 14. C3×C9×A4 | C2×C3 | semidirect |
| 20. C9⋊S4 | C32 | direct (N × H) |
| 32. C32×A4 | D9 | semidirect |
| 36. C22×C3×C9 | C3×D3 | semidirect |
| 39. C3×C22⋊C9 | C3×D3 | semidirect |
| 44. C9×A4 | C2×C32 | semidirect |
| 52. C32×C9 | S4 | semidirect |
| 70. C22×C32 | C3⋊D9 | semidirect |
| 77. C3×A4 | C3×D9 | semidirect |
| 82. C22×C9 | C32×D3 | semidirect |
| 85. C22⋊C9 | C32×D3 | semidirect |
| 100. C3×C9 | C3×S4 | semidirect |
| 117. C22×C3 | C3×C3⋊D9 | semidirect |
| 121. A4 | C32×D9 | semidirect |
| 131. C32 | C9⋊S4 | direct (N × H) |
| 136. C9 | C32×S4 | semidirect |
| 145. C22 | C32×C3⋊D9 | semidirect |
| 150. C3 | C3×C9⋊S4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×A4 | 2 |
| C32×C3⋊S4 | 3 |
| C3×C9⋊S4 | 3 |
| C32×(C22⋊C9)⋊C2 | 3 |
| C32×#611 | 3 |
| C32×C3⋊D9 | 4 |