Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92309 |
| commutator, hypocenter | C92 | C2×C3×C4 |
| Frattini, socle | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C4×#6896 | C2 |
| prime radical | C2×#92309 | C2 |
| cosocle | C2×C92 | C22×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#6896 | C2 | semidirect |
| 3. #11757613 | C2 | semidirect |
| 5. C4×C9⋊D9 | C3 | semidirect |
| 8. #92309 | C4 | direct (N × H) |
| 17. C4×C92 | C2×C3 | semidirect |
| 18. C9⋊Dic9 | C2×C3 | semidirect |
| 20. #6896 | C2×C4 | semidirect |
| 31. C9⋊D9 | C3×C4 | semidirect |
| 51. C92 | C2×C3×C4 | semidirect |
| 81. C4×C9 | AGL(1,ℤ/9) | semidirect |
| 120. C9 | C4×AGL(1,ℤ/9) | semidirect |
| 130. C4 | #92309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92309 | 2 |
| C4×#6896 | 2 |
| #11757613 | 2 |
| C4×C3⋊AGL(1,ℤ/9) | 3 |
| C4×C9⋊D9 | 3 |
| C4×#4169 | 3 |