Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
260 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×C8×C9 | C2 | semidirect |
| 3. C3×C9×C3⋊C8 | C2 | semidirect |
| 6. C9×ΓL(1,𝔽25) | C3 | direct (N × H) |
| 18. C3×C8×C9 | D3 | semidirect |
| 19. C3×C8×C9 | C2×C3 | semidirect |
| 20. C9×C3⋊C8 | C2×C3 | semidirect |
| 24. C3×ΓL(1,𝔽25) | C9 | direct (N × H) |
| 38. C32×C9 | M16 | semidirect |
| 45. C32×C8 | C2×C9 | semidirect |
| 48. C3×C3⋊C8 | C2×C9 | semidirect |
| 53. C8×C9 | C3×D3 | semidirect |
| 64. ΓL(1,𝔽25) | C3×C9 | direct (N × H) |
| 83. C3×C9 | ΓL(1,𝔽25) | direct (N × H) |
| 84. C3×C9 | C3×M16 | semidirect |
| 92. C3×C8 | D3×C9 | semidirect |
| 93. C3×C8 | C2×C3×C9 | semidirect |
| 95. C3⋊C8 | C2×C3×C9 | semidirect |
| 121. C32 | C9×M16 | semidirect |
| 125. C9 | C3×ΓL(1,𝔽25) | direct (N × H) |
| 128. C8 | C3×D3×C9 | semidirect |
| 142. C3 | C9×ΓL(1,𝔽25) | direct (N × H) |
| 143. C3 | C3×C9×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D3×C9 | 2 |
| C32×C8×C9 | 2 |
| C3×C9×C3⋊C8 | 2 |
| C32×ΓL(1,𝔽25) | 3 |
| C3×C9×M16 | 3 |
| C9×ΓL(1,𝔽25) | 3 |