Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
200 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 200 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 |
|---|---|---|
| 1. D3×Q8×C9 | C2 | semidirect |
| 3. C3×C9×SD16 | C2 | semidirect |
| 4. C9×#216 | C2 | semidirect |
| 5. C9×#214 | C2 | semidirect |
| 6. C9×Dic12 | C2 | semidirect |
| 7. C9×ΓL(1,𝔽25) | C2 | semidirect |
| 34. C9×SD16 | D3 | semidirect |
| 44. #915 | C9 | direct (N × H) |
| 75. D3×Q8 | C2×C9 | semidirect |
| 81. C3×SD16 | C2×C9 | semidirect |
| 84. #216 | C2×C9 | semidirect |
| 85. #214 | C2×C9 | semidirect |
| 86. Dic12 | C2×C9 | semidirect |
| 87. ΓL(1,𝔽25) | C2×C9 | semidirect |
| 106. C3×C9 | #137 | semidirect |
| 145. SD16 | D3×C9 | semidirect |
| 166. C9 | #915 | direct (N × H) |
| 194. C3 | C9×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×C9 | 2 |
| C9×#237 | 2 |
| C3×C9×SD16 | 2 |
| C9×#216 | 2 |
| C9×#214 | 2 |
| C9×Dic12 | 2 |
| C9×ΓL(1,𝔽25) | 2 |
| C3×#915 | 3 |
| C9×#137 | 3 |