Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
651 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 651 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | C3⋊S4 |
| commutator, hypocenter | C3×A4 | C2×C3×C9 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3×D3 |
| prime radical | C32×C3⋊S4 | C3 |
| cosocle | C32×A4 | C2×C32 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C3×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C9×A4 | C2 | semidirect |
| 3. C9×C3⋊S4 | C3 | direct (N × H) |
| 8. C22×C32×C9 | D3 | semidirect |
| 14. C3×C9×A4 | D3 | semidirect |
| 15. C3×C9×A4 | C2×C3 | semidirect |
| 18. C3×C3⋊S4 | C9 | direct (N × H) |
| 36. C32×A4 | C2×C9 | semidirect |
| 43. C22×C3×C9 | C3×D3 | semidirect |
| 44. C22×C3×C9 | C3⋊D3 | semidirect |
| 52. C9×A4 | C3×D3 | semidirect |
| 62. C32×C9 | S4 | semidirect |
| 63. C3⋊S4 | C3×C9 | direct (N × H) |
| 85. C22×C32 | D3×C9 | semidirect |
| 98. C3×A4 | D3×C9 | semidirect |
| 99. C3×A4 | C2×C3×C9 | semidirect |
| 106. C22×C9 | C3×C3⋊D3 | semidirect |
| 126. C3×C9 | C3×S4 | semidirect |
| 127. C3×C9 | C3⋊S4 | direct (N × H) |
| 150. C22×C3 | C3×D3×C9 | semidirect |
| 151. C22×C3 | C9×C3⋊D3 | semidirect |
| 156. A4 | C3×D3×C9 | semidirect |
| 173. C32 | C9×S4 | semidirect |
| 178. C9 | C3×C3⋊S4 | direct (N × H) |
| 190. C22 | C3×C9×C3⋊D3 | semidirect |
| 197. C3 | C3×C9×S4 | semidirect |
| 198. C3 | C9×C3⋊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 |
| C9×C3⋊S4 | 3 |
| C3×C9×S4 | 3 |
| C3×C9×#67 | 3 |
| C3×C9×C3⋊D3 | 4 |