Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
206 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 92 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. C2×C3×C9⋊C8 | C2 | semidirect |
| 4. C3×#3663 | C2 | semidirect |
| 5. C3×C8×D9 | C2 | semidirect |
| 7. #63469 | C3 | direct (N × H) |
| 23. C9×M16 | C2×C3 | semidirect |
| 24. C2×C9⋊C8 | C2×C3 | semidirect |
| 25. #3663 | C2×C3 | semidirect |
| 26. C8×D9 | C2×C3 | semidirect |
| 59. C3×M16 | D9 | semidirect |
| 80. C3×C9 | #131 | semidirect |
| 109. M16 | C3×D9 | semidirect |
| 127. C9 | C3×#131 | semidirect |
| 150. C3 | #63469 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3697 | 2 |
| C3×C9×M16 | 2 |
| C2×C3×C9⋊C8 | 2 |
| C3×#3663 | 2 |
| C3×C8×D9 | 2 |
| C3×#907 | 3 |
| #63469 | 3 |