Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
628 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11758088 |
| commutator, hypocenter | C33×C9 | C2×C4 |
| Frattini | C2×C3 | C3⋊#1113 |
| Fitting, cosocle | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| prime radical | C2×C32×C3⋊D9 | C2 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C3×C3⋊(C3⋊Dic9) | C2 | semidirect |
| 8. C32×C3⋊D9 | C4 | semidirect |
| 15. C3⋊(C3⋊Dic9) | D3 | semidirect |
| 21. C33×C9 | C2×C4 | semidirect |
| 35. C3×C3⋊D9 | Dic3 | semidirect |
| 43. C3⋊(C3⋊Dic3) | D9 | semidirect |
| 65. C32×C9 | C4×D3 | semidirect |
| 66. C32×C9 | C2×Dic3 | semidirect |
| 92. C3⋊D9 | C3⋊Dic3 | semidirect |
| 121. C33 | C4×D9 | semidirect |
| 131. C3×C9 | D3×Dic3 | semidirect |
| 132. C3×C9 | C2×C3⋊Dic3 | semidirect |
| 179. C32 | Dic3×D9 | semidirect |
| 180. C32 | (C3⋊D9)⋊C4 | semidirect |
| 186. C9 | D3×C3⋊Dic3 | semidirect |
| 206. C3 | D9×C3⋊Dic3 | semidirect |
| 207. C3 | #10619896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C3⋊D9 | 2 |
| C9×C3⋊(C3⋊Dic3) | 2 |
| C3×C3⋊(C3⋊Dic9) | 2 |
| #10620155 | 3 |
| #10619896 | 3 |
| D9×C3⋊Dic3 | 3 |