Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
412 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 3. Q8×Q8⋊C9 | C3 | direct (N × H) |
| 12. C3×Q8⋊C9 | Q8 | direct (N × H) |
| 13. C3×Q82 | C9 | semidirect |
| 40. Q8⋊C9 | C3×Q8 | direct (N × H) |
| 41. Q82 | C3×C9 | semidirect |
| 72. C3×Q8 | Q8⋊C9 | direct (N × H) |
| 73. C3×Q8 | Q8×C9 | semidirect |
| 108. Q8 | C3×Q8⋊C9 | direct (N × H) |
| 109. Q8 | C3×Q8×C9 | semidirect |
| 124. C3 | Q8×Q8⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Q8⋊C9 | 2 |
| C32×Q82 | 3 |
| Q8×Q8⋊C9 | 3 |
| C2×C3×Q8×C9 | 4 |