Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
224 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 117 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. C3×C9×M16 | C2 | semidirect |
| 3. C9×#208 | C2 | semidirect |
| 4. C9×ΓL(1,𝔽25) | C2 | semidirect |
| 5. D3×C8×C9 | C2 | semidirect |
| 15. C3×C8×C9 | C22 | semidirect |
| 16. C9×C3⋊C8 | C22 | semidirect |
| 26. C9×M16 | D3 | direct (N × H) |
| 37. D3×M16 | C9 | direct (N × H) |
| 57. C8×C9 | C2×D3 | semidirect |
| 61. D3×C9 | M16 | direct (N × H) |
| 67. C3×M16 | C2×C9 | semidirect |
| 70. #208 | C2×C9 | semidirect |
| 71. ΓL(1,𝔽25) | C2×C9 | semidirect |
| 72. D3×C8 | C2×C9 | semidirect |
| 93. C3×C9 | C2×M16 | semidirect |
| 111. C3×C8 | C22×C9 | semidirect |
| 113. C3⋊C8 | C22×C9 | semidirect |
| 127. M16 | D3×C9 | direct (N × H) |
| 150. C9 | D3×M16 | direct (N × H) |
| 159. C8 | C2×D3×C9 | semidirect |
| 169. D3 | C9×M16 | direct (N × H) |
| 179. C3 | C2×C9×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C3×C9×M16 | 2 |
| C9×#208 | 2 |
| C9×ΓL(1,𝔽25) | 2 |
| D3×C8×C9 | 2 |
| C3×D3×M16 | 3 |
| C2×C9×M16 | 3 |