Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C3×#41⋊C9 | C2 | semidirect |
| 2. C3×C4×Q8⋊C9 | C2 | semidirect |
| 4. C4⋊(#41⋊C9) | C3 | direct (N × H) |
| 13. C2×#41⋊C9 | C2×C3 | semidirect |
| 14. C4×Q8⋊C9 | C2×C3 | semidirect |
| 17. C3×Q8⋊C9 | D4 | semidirect |
| 18. C3×#550 | C9 | semidirect |
| 62. Q8⋊C9 | C3×D4 | semidirect |
| 63. #550 | C3×C9 | semidirect |
| 167. C3×C4 | #41⋊C9 | semidirect |
| 200. C4 | C3×#41⋊C9 | semidirect |
| 201. C3 | C4⋊(#41⋊C9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41⋊C9 | 2 |
| C3×C4×Q8⋊C9 | 2 |
| C32×#550 | 3 |
| C4⋊(#41⋊C9) | 3 |
| C3×C9×C4⋊C4 | 4 |