Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
260 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D3×#157 |
| commutator, hypocenter | C33 | C2×C4×C9 |
| Frattini | C3 | C3×D3×#157 |
| Fitting | C33×C9 | C2×C4 |
| socle | C34 | C2×C3×C4 |
| prime radical | C3×D3×C3⋊D3 | C2×C3 |
| cosocle | C32×C3⋊D3 | C22×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×C3⋊#157 | C2 | semidirect |
| 3. C3×C9×#157 | C2 | semidirect |
| 6. C9×C3⋊(C3⋊D3) | C4 | semidirect |
| 8. C32×D3×C9 | C4 | semidirect |
| 16. C9×#157 | D3 | direct (N × H) |
| 17. C33×C9 | C2×C4 | semidirect |
| 19. D3×#157 | C9 | direct (N × H) |
| 36. C3⋊#157 | C2×C9 | semidirect |
| 39. C3×#157 | C2×C9 | semidirect |
| 51. C32×C9 | C4×D3 | semidirect |
| 56. C3⋊(C3⋊D3) | C4×C9 | semidirect |
| 66. C32×D3 | C4×C9 | semidirect |
| 76. D3×C9 | #157 | direct (N × H) |
| 82. #157 | D3×C9 | direct (N × H) |
| 94. C33 | C2×C4×C9 | semidirect |
| 105. C3×C9 | C2×#157 | semidirect |
| 149. C32 | C4×D3×C9 | semidirect |
| 154. C9 | D3×#157 | direct (N × H) |
| 167. D3 | C9×#157 | direct (N × H) |
| 176. C3 | C2×C9×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C9×C3⋊D3 | 2 |
| C9×C3⋊#157 | 2 |
| C3×C9×#157 | 2 |
| C3×D3×#157 | 3 |
| C2×C9×#157 | 3 |
| C4×D3×C9 | 9 |