Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 39 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. SL(2,𝔽3)×Dic9 | C2 | semidirect |
| 3. C9×#859 | C2 | semidirect |
| 8. C9⋊GL(2,𝔽3) | C4 | semidirect |
| 13. Q8×Dic9 | D3 | semidirect |
| 23. C9×SL(2,𝔽3) | C2×C4 | semidirect |
| 55. #859 | D9 | semidirect |
| 68. Q8×C9 | C4×D3 | semidirect |
| 118. Dic9 | GL(2,𝔽3) | semidirect |
| 143. SL(2,𝔽3) | C4×D9 | semidirect |
| 190. C9 | C4×GL(2,𝔽3) | semidirect |
| 193. Q8 | (C3⋊D9)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊GL(2,𝔽3) | 2 |
| SL(2,𝔽3)×Dic9 | 2 |
| C9×#859 | 2 |
| #10593214 | 3 |
| #10588468 | 3 |
| C2×(C3⋊D9)⋊C4 | 4 |