Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
759 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 759 conjugacy classes of subgroups — too many to draw. Only its 292 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 |
|---|---|---|
| 3. #10592634 | C3 | semidirect |
| 7. C42×H(3,𝔽3) | C4 | semidirect |
| 28. C32×C42 | Dic3 | semidirect |
| 29. C32×C42 | C3×C4 | semidirect |
| 35. C4×H(3,𝔽3) | C4⋊C4 | semidirect |
| 86. C32×C4 | C4⋊Dic3 | semidirect |
| 87. C32×C4 | C3×C4⋊C4 | semidirect |
| 92. H(3,𝔽3) | #384 | semidirect |
| 124. C42 | (C3⋊Dic3)⋊C3 | semidirect |
| 145. C32 | #4935 | semidirect |
| 146. C32 | C3×#384 | semidirect |
| 168. C4 | C4⋊((C3⋊Dic3)⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×H(3,𝔽3) | 2 |
| C2×C4⋊((C3⋊Dic3)⋊C3) | 2 |
| #10592634 | 3 |
| C3×#4935 | 3 |