Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 77 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)×C3⋊Dic3 | C2 | semidirect |
| 3. C3⋊(C3⋊#859) | C2 | semidirect |
| 7. C32×GL(2,𝔽3) | C4 | semidirect |
| 11. Q8×C3⋊Dic3 | D3 | semidirect |
| 23. C32×SL(2,𝔽3) | C2×C4 | semidirect |
| 31. C3×GL(2,𝔽3) | Dic3 | semidirect |
| 73. C3×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 86. GL(2,𝔽3) | C3⋊Dic3 | semidirect |
| 136. SL(2,𝔽3) | C2×C3⋊Dic3 | semidirect |
| 180. C32 | #5394 | semidirect |
| 215. C3 | #10593204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×GL(2,𝔽3) | 2 |
| SL(2,𝔽3)×C3⋊Dic3 | 2 |
| C3⋊(C3⋊#859) | 2 |
| #10593204 | 3 |
| #10592863 | 3 |
| (C2×D3)⋊(C3⋊Dic3) | 4 |