Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
242 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 6. #63506 | C3 | direct (N × H) |
| 26. C3×Dic9 | Q8 | semidirect |
| 67. Dic9 | C3×Q8 | semidirect |
| 69. C3×C9 | C4⋊Q8 | semidirect |
| 110. C9 | C3×C4⋊Q8 | semidirect |
| 129. C3 | #63506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C2×C3×Dic18 | 2 |
| C3×Dic9⋊C4 | 2 |
| C3×C4×Dic9 | 2 |
| C3×#944 | 3 |
| #63506 | 3 |