Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
744 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 186 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×C4 | C3⋊D9 |
| commutator, hypocenter | C3×C9 | C32×C8 |
| Frattini | C3×C4 | C32×C3⋊D3 |
| Fitting | C33×C4×C9 | C2 |
| socle, prime radical | C2×C34 | Dic3 |
| cosocle | C3×C4×C9 | C2×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C32×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×C3⋊(C9⋊C8) | C3 | direct (N × H) |
| 11. C33×C9 | C8 | semidirect |
| 15. C3⋊(C9⋊C8) | C32 | direct (N × H) |
| 36. C32×C9 | C3⋊C8 | semidirect |
| 37. C32×C9 | C3×C8 | semidirect |
| 67. C33 | C9⋊C8 | semidirect |
| 74. C3×C9 | C3×C3⋊C8 | semidirect |
| 75. C3×C9 | C32×C8 | semidirect |
| 100. C32 | C3×C9⋊C8 | semidirect |
| 101. C32 | C3⋊(C9⋊C8) | direct (N × H) |
| 105. C9 | C32×C3⋊C8 | semidirect |
| 115. C3 | C32×C9⋊C8 | semidirect |
| 116. C3 | C3×C3⋊(C9⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×C9 | 2 |
| C32×C3⋊(C3⋊C8) | 3 |
| C3×C3⋊(C9⋊C8) | 3 |
| C32×C9⋊C8 | 3 |