Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C4×C9⋊SL(2,𝔽3) | C2 | semidirect |
| 4. C4×C9×#41 | C3 | semidirect |
| 5. C4×#41⋊C9 | C3 | semidirect |
| 6. #88683 | C4 | direct (N × H) |
| 20. C9⋊SL(2,𝔽3) | C2×C4 | semidirect |
| 27. C9×#41 | C3×C4 | semidirect |
| 32. #41⋊C9 | C3×C4 | semidirect |
| 68. C4×#41 | 3−1+2 | semidirect |
| 98. C4×C9 | #41⋊C3 | semidirect |
| 128. #41 | C4×3−1+2 | semidirect |
| 151. C9 | C4×#41⋊C3 | semidirect |
| 176. C4 | #88683 | direct (N × H) |
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 |
| C4×C9×#41 | 3 |
| C4×#41⋊C9 | 3 |
| C42×3−1+2 | 4 |