Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
314 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 62 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×C22⋊(Q8⋊C9) | C2 | semidirect |
| 3. #393⋊C9 | C3 | direct (N × H) |
| 7. C22⋊(Q8⋊C9) | C2×C3 | semidirect |
| 12. C3×#393 | C9 | semidirect |
| 22. C22×C3×Q8 | C2×C9 | semidirect |
| 41. #393 | C3×C9 | semidirect |
| 64. C22×Q8 | C2×C3×C9 | semidirect |
| 72. C23×C3 | Q8⋊C9 | semidirect |
| 119. C23 | C3×Q8⋊C9 | semidirect |
| 143. C3 | #393⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊(Q8⋊C9) | 2 |
| C32×#393 | 3 |
| #393⋊C9 | 3 |
| C22×C3×C22⋊C9 | 4 |