Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
208 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×C3×C8×C9 | C2 | semidirect |
| 3. C9×#208 | C2 | semidirect |
| 4. C9×ΓL(1,𝔽25) | C2 | semidirect |
| 5. D3×C8×C9 | C2 | semidirect |
| 26. C2×C8×C9 | D3 | semidirect |
| 33. #901 | C9 | direct (N × H) |
| 62. C2×C3×C8 | C2×C9 | semidirect |
| 64. #208 | C2×C9 | semidirect |
| 65. ΓL(1,𝔽25) | C2×C9 | semidirect |
| 66. D3×C8 | C2×C9 | semidirect |
| 81. C3×C9 | #131 | semidirect |
| 113. C2×C8 | D3×C9 | semidirect |
| 129. C9 | #901 | direct (N × H) |
| 152. C3 | C9×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#235 | 2 |
| C2×C3×C8×C9 | 2 |
| C9×#208 | 2 |
| C9×ΓL(1,𝔽25) | 2 |
| D3×C8×C9 | 2 |
| C3×#901 | 3 |
| C9×#131 | 3 |