Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 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. D3×Q8×C9 | C2 | semidirect |
| 3. C3×C9×Q16 | C2 | semidirect |
| 4. C9×#216 | C2 | semidirect |
| 5. C9×#215 | C2 | semidirect |
| 6. C9×#204 | C2 | semidirect |
| 7. C9×ΓL(1,𝔽25) | C2 | semidirect |
| 32. C9×Q16 | D3 | semidirect |
| 44. #918 | C9 | direct (N × H) |
| 76. D3×Q8 | C2×C9 | semidirect |
| 79. C3×Q16 | C2×C9 | semidirect |
| 84. #216 | C2×C9 | semidirect |
| 85. #215 | C2×C9 | semidirect |
| 86. #204 | C2×C9 | semidirect |
| 87. ΓL(1,𝔽25) | C2×C9 | semidirect |
| 106. C3×C9 | #137 | semidirect |
| 142. Q16 | D3×C9 | semidirect |
| 165. C9 | #918 | direct (N × H) |
| 192. C3 | C9×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#239 | 2 |
| D3×Q8×C9 | 2 |
| C3×C9×Q16 | 2 |
| C9×#216 | 2 |
| C9×#215 | 2 |
| C9×#204 | 2 |
| C9×ΓL(1,𝔽25) | 2 |
| C3×#918 | 3 |
| C9×#137 | 3 |