Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
320 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 320 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. C22×C9⋊SL(2,𝔽3) | C2 | semidirect |
| 3. C4×C9⋊SL(2,𝔽3) | C2 | semidirect |
| 5. C9×#548 | C3 | semidirect |
| 6. #548⋊C9 | C3 | semidirect |
| 14. C2×C9×#41 | C2×C3 | semidirect |
| 16. C2×#41⋊C9 | C2×C3 | semidirect |
| 21. C4×Q8×C9 | C2×C3 | semidirect |
| 23. C4×Q8⋊C9 | C2×C3 | semidirect |
| 27. C9⋊SL(2,𝔽3) | D4 | semidirect |
| 96. #548 | 3−1+2 | semidirect |
| 136. C22×C9 | #41⋊C3 | semidirect |
| 146. C2×#41 | C2×3−1+2 | semidirect |
| 151. C4×Q8 | C2×3−1+2 | semidirect |
| 226. C9 | #548⋊C3 | semidirect |
| 259. C22 | #88683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88683 | 2 |
| C22×C9⋊SL(2,𝔽3) | 2 |
| C4×C9⋊SL(2,𝔽3) | 2 |
| C3×#548⋊C3 | 3 |
| C9×#548 | 3 |
| #548⋊C9 | 3 |
| C22⋊C4×3−1+2 | 4 |