Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
260 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 36 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 | D9×#157 |
| commutator, hypocenter | C32×C9 | C2×C3×C4 |
| Frattini | C3 | C3×D3×#157 |
| Fitting | C33×C9 | C2×C4 |
| socle | C34 | C4×D3 |
| prime radical | C3×D9×C3⋊D3 | C2 |
| cosocle | C9×C3⋊D3 | C22×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C9⋊#157 | C2 | semidirect |
| 3. C3×C9×#157 | C2 | semidirect |
| 5. D9×#157 | C3 | direct (N × H) |
| 6. C3×C3⋊(C3⋊D9) | C4 | semidirect |
| 8. C33×D9 | C4 | semidirect |
| 14. C9⋊#157 | C2×C3 | semidirect |
| 16. C9×#157 | C2×C3 | semidirect |
| 17. C33×C9 | C2×C4 | semidirect |
| 24. C3⋊(C3⋊D9) | C3×C4 | semidirect |
| 32. C32×D9 | C3×C4 | semidirect |
| 39. C3×#157 | D9 | direct (N × H) |
| 51. C32×C9 | C2×C3×C4 | semidirect |
| 76. C3×D9 | #157 | direct (N × H) |
| 82. #157 | C3×D9 | direct (N × H) |
| 94. C33 | C4×D9 | semidirect |
| 105. C3×C9 | C2×#157 | semidirect |
| 129. D9 | C3×#157 | direct (N × H) |
| 149. C32 | C3×C4×D9 | semidirect |
| 154. C9 | C2×C3×#157 | semidirect |
| 176. C3 | D9×#157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D9×C3⋊D3 | 2 |
| C3×C9⋊#157 | 2 |
| C3×C9×#157 | 2 |
| C3×D3×#157 | 3 |
| D9×#157 | 3 |
| C3×C4×D9 | 9 |