Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
327 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 51 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. C22×C9×SL(2,𝔽3) | C2 | semidirect |
| 2. C2×C9×GL(2,𝔽3) | C2 | semidirect |
| 3. C9×#859 | C2 | semidirect |
| 13. C22×Q8×C9 | D3 | semidirect |
| 25. C9×SL(2,𝔽3) | D4 | semidirect |
| 26. #5421 | C9 | direct (N × H) |
| 58. C22×SL(2,𝔽3) | C2×C9 | semidirect |
| 59. C2×GL(2,𝔽3) | C2×C9 | semidirect |
| 63. #859 | C2×C9 | semidirect |
| 78. Q8×C9 | #67 | semidirect |
| 133. C22×C9 | GL(2,𝔽3) | semidirect |
| 139. C22×Q8 | D3×C9 | semidirect |
| 167. SL(2,𝔽3) | D4×C9 | semidirect |
| 223. C9 | #5421 | direct (N × H) |
| 229. Q8 | C9×#67 | semidirect |
| 259. C22 | C9×GL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×SL(2,𝔽3) | 2 |
| C2×C9×GL(2,𝔽3) | 2 |
| C9×#859 | 2 |
| C3×#5421 | 3 |
| C9×#448 | 3 |
| C2×C9×#67 | 4 |