Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
636 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92309 |
| commutator, cosocle, hypocenter | C92 | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×#6896 | C2 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6896 | C2 | semidirect |
| 2. C2×#92309 | C2 | direct (N × H) |
| 4. C22×C9⋊D9 | C3 | semidirect |
| 6. C2×#6896 | C22 | semidirect |
| 7. #92309 | C22 | direct (N × H) |
| 13. C22×C92 | C2×C3 | semidirect |
| 14. C2×C9⋊D9 | C2×C3 | semidirect |
| 16. #6896 | C23 | semidirect |
| 26. C2×C92 | C22×C3 | semidirect |
| 27. C9⋊D9 | C22×C3 | semidirect |
| 43. C92 | C23×C3 | semidirect |
| 68. C22×C9 | AGL(1,ℤ/9) | semidirect |
| 89. C2×C9 | C2×AGL(1,ℤ/9) | semidirect |
| 104. C9 | C22×AGL(1,ℤ/9) | semidirect |
| 113. C22 | #92309 | direct (N × H) |
| 118. C2 | C2×#92309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6896 | 2 |
| C2×#92309 | 2 |
| C22×C3⋊AGL(1,ℤ/9) | 3 |
| C22×C9⋊D9 | 3 |
| C22×#4169 | 3 |