Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
198 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 68 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×Q8×D9 | C2 | semidirect |
| 3. C3×C9×Q16 | C2 | semidirect |
| 4. C3×#3675 | C2 | semidirect |
| 5. C3×#3674 | C2 | semidirect |
| 6. C3×#3664 | C2 | semidirect |
| 7. C3×#3663 | C2 | semidirect |
| 9. #63480 | C3 | direct (N × H) |
| 29. Q8×D9 | C2×C3 | semidirect |
| 31. C9×Q16 | C2×C3 | semidirect |
| 32. #3675 | C2×C3 | semidirect |
| 33. #3674 | C2×C3 | semidirect |
| 34. #3664 | C2×C3 | semidirect |
| 35. #3663 | C2×C3 | semidirect |
| 79. C3×Q16 | D9 | semidirect |
| 106. C3×C9 | #137 | semidirect |
| 142. Q16 | C3×D9 | semidirect |
| 165. C9 | C3×#137 | semidirect |
| 192. C3 | #63480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3701 | 2 |
| C3×Q8×D9 | 2 |
| C3×C9×Q16 | 2 |
| C3×#3675 | 2 |
| C3×#3674 | 2 |
| C3×#3664 | 2 |
| C3×#3663 | 2 |
| C3×#918 | 3 |
| #63480 | 3 |