Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
| 15. C4×Q8⋊C9 | D3 | semidirect |
| 18. C3×Q8⋊C9 | D4 | semidirect |
| 20. #5577 | C9 | semidirect |
| 67. Q8⋊C9 | D12 | semidirect |
| 189. C3×C4 | #41⋊C9 | semidirect |
| 227. C4 | C3⋊(#41⋊C9) | semidirect |
| 229. C3 | C4⋊(#41⋊C9) | semidirect |
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 |
| C3×#5577 | 3 |
| C4⋊(#41⋊C9) | 3 |
| C9×C4⋊Dic3 | 4 |