Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
242 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 26. C9×Dic3 | Q8 | semidirect |
| 28. #944 | C9 | direct (N × H) |
| 69. C3×C9 | C4⋊Q8 | semidirect |
| 107. Dic3 | Q8×C9 | semidirect |
| 110. C9 | #944 | direct (N × H) |
| 129. C3 | C9×C4⋊Q8 | semidirect |
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×C9×Dic6 | 2 |
| C9×Dic3⋊C4 | 2 |
| C4×C9×Dic3 | 2 |
| C3×#944 | 3 |
| C9×C4⋊Q8 | 3 |