Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
226 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C3×C9⋊C8 | C2 | semidirect |
| 4. C3×#3663 | C2 | direct (N × H) |
| 6. C2×#3663 | C3 | direct (N × H) |
| 12. C3×C8×C9 | C22 | semidirect |
| 13. C3×C9⋊C8 | C22 | semidirect |
| 20. C2×C8×C9 | C2×C3 | semidirect |
| 21. C2×C9⋊C8 | C2×C3 | semidirect |
| 22. #3663 | C2×C3 | direct (N × H) |
| 45. C8×C9 | C22×C3 | semidirect |
| 46. C9⋊C8 | C22×C3 | semidirect |
| 47. C2×C3×C9 | M16 | semidirect |
| 55. C2×C3×C8 | D9 | semidirect |
| 75. C3×C9 | C2×M16 | semidirect |
| 89. C3×C8 | C2×D9 | semidirect |
| 97. C2×C9 | C3×M16 | semidirect |
| 103. C2×C8 | C3×D9 | semidirect |
| 121. C9 | C2×C3×M16 | semidirect |
| 128. C8 | C2×C3×D9 | semidirect |
| 132. C2×C3 | #3663 | direct (N × H) |
| 144. C3 | C2×#3663 | direct (N × H) |
| 147. C2 | C3×#3663 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D9 | 2 |
| C2×C3×C8×C9 | 2 |
| C2×C3×C9⋊C8 | 2 |
| C3×#3663 | 2 |
| C2×C3×ΓL(1,𝔽25) | 3 |
| C2×#3663 | 3 |