Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
303 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 75 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×#88683 | C2 | semidirect |
| 2. C4×C9⋊SL(2,𝔽3) | C2 | semidirect |
| 4. C9×#550 | C3 | semidirect |
| 5. C4⋊(#41⋊C9) | C3 | semidirect |
| 20. C9⋊SL(2,𝔽3) | D4 | semidirect |
| 69. #550 | 3−1+2 | semidirect |
| 101. C4×C9 | #41⋊C3 | semidirect |
| 159. C9 | C4⋊(#41⋊C3) | semidirect |
| 188. C4 | #88683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88683 | 2 |
| C4×C9⋊SL(2,𝔽3) | 2 |
| C3×C4⋊(#41⋊C3) | 3 |
| C9×#550 | 3 |
| C4⋊(#41⋊C9) | 3 |
| C4⋊C4×3−1+2 | 4 |