Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
394 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #92265⋊C2 |
| commutator, cosocle, hypocenter | C92 | C23×C3 |
| Frattini | C32 | C2×C3×D32 |
| Fitting | C2×#6900 | C22 |
| socle | C2×C32 | C3×D32 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92314 | C2 | semidirect |
| 2. C2×#92265 | C2 | semidirect |
| 3. #92265⋊C2 | C2 | direct (N × H) |
| 5. C2×D92 | C3 | semidirect |
| 6. C2×#6900 | C22 | semidirect |
| 7. #92314 | C22 | semidirect |
| 8. #92265 | C22 | semidirect |
| 14. C2×C9⋊D9 | C2×C3 | semidirect |
| 16. C2×C9×D9 | C2×C3 | semidirect |
| 17. D92 | C2×C3 | semidirect |
| 18. #6900 | C23 | semidirect |
| 30. C2×C92 | C22×C3 | semidirect |
| 31. C9⋊D9 | C22×C3 | semidirect |
| 33. C9×D9 | C22×C3 | semidirect |
| 53. C92 | C23×C3 | semidirect |
| 91. C2×D9 | AGL(1,ℤ/9) | semidirect |
| 117. C2×C9 | C2×AGL(1,ℤ/9) | semidirect |
| 121. D9 | C2×AGL(1,ℤ/9) | semidirect |
| 137. C9 | C22×AGL(1,ℤ/9) | semidirect |
| 156. C2 | #92265⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92314 | 2 |
| C2×#92265 | 2 |
| #92265⋊C2 | 2 |
| C2×D3×AGL(1,ℤ/9) | 3 |
| C2×D92 | 3 |