Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
313 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 313 conjugacy classes of subgroups — too many to draw. Only its 49 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. C9⋊#859 | C2 | semidirect |
| 3. C9×#859 | C2 | semidirect |
| 8. D9×SL(2,𝔽3) | C4 | semidirect |
| 23. C9×SL(2,𝔽3) | C2×C4 | semidirect |
| 32. Q8×D9 | Dic3 | semidirect |
| 55. #859 | D9 | direct (N × H) |
| 67. Q8×C9 | C2×Dic3 | semidirect |
| 145. SL(2,𝔽3) | C4×D9 | semidirect |
| 158. D9 | #859 | direct (N × H) |
| 190. C9 | C2×#859 | semidirect |
| 195. Q8 | Dic3×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×SL(2,𝔽3) | 2 |
| C9⋊#859 | 2 |
| C9×#859 | 2 |
| D3×#859 | 3 |
| D9×#103 | 3 |
| C2×Dic3×D9 | 4 |