Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
206 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 206 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 |
|---|---|---|
| 1. C3×#3701 | C2 | semidirect |
| 2. C3×#3699 | C2 | semidirect |
| 3. C3×C9×SD16 | C2 | semidirect |
| 4. C3×#3674 | C2 | semidirect |
| 5. C3×#3673 | C2 | semidirect |
| 6. C3×#3664 | C2 | semidirect |
| 7. C3×C8×D9 | C2 | semidirect |
| 9. #63478 | C3 | direct (N × H) |
| 28. #3701 | C2×C3 | semidirect |
| 29. #3699 | C2×C3 | semidirect |
| 31. C9×SD16 | C2×C3 | semidirect |
| 32. #3674 | C2×C3 | semidirect |
| 33. #3673 | C2×C3 | semidirect |
| 34. #3664 | C2×C3 | semidirect |
| 35. C8×D9 | C2×C3 | semidirect |
| 81. C3×SD16 | D9 | semidirect |
| 107. C3×C9 | #135 | semidirect |
| 147. SD16 | C3×D9 | semidirect |
| 169. C9 | C3×#135 | semidirect |
| 199. C3 | #63478 | 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×#3699 | 2 |
| C3×C9×SD16 | 2 |
| C3×#3674 | 2 |
| C3×#3673 | 2 |
| C3×#3664 | 2 |
| C3×C8×D9 | 2 |
| C3×#916 | 3 |
| #63478 | 3 |