Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1979 conjugacy classes of subgroups; only the 619 normal subgroups are shown.
This group has 1979 conjugacy classes of subgroups — too many to draw. Only its 619 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. C2×#88447 | C2 | direct (N × H) |
| 6. C22×#1084 | C4 | semidirect |
| 8. C22×(C3⋊Dic3)⋊C3 | C4 | semidirect |
| 10. #88447 | C22 | direct (N × H) |
| 19. C2×#1084 | C2×C4 | semidirect |
| 21. C2×(C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 27. C22×C3⋊Dic3 | Dic3 | semidirect |
| 36. C22×H(3,𝔽3) | C42 | semidirect |
| 40. #1084 | C22×C4 | semidirect |
| 41. (C3⋊Dic3)⋊C3 | C22×C4 | semidirect |
| 57. C2×C3⋊Dic3 | C2×Dic3 | semidirect |
| 66. C2×H(3,𝔽3) | C2×C42 | semidirect |
| 90. C22×C32 | C4×Dic3 | semidirect |
| 95. C3⋊Dic3 | C22×Dic3 | semidirect |
| 102. H(3,𝔽3) | C22×C42 | semidirect |
| 128. C2×C32 | C2×C4×Dic3 | semidirect |
| 158. C32 | C22×C4×Dic3 | semidirect |
| 176. C22 | #88447 | direct (N × H) |
| 185. C2 | C2×#88447 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1084 | 2 |
| C23×(C3⋊Dic3)⋊C3 | 2 |
| C2×#88447 | 2 |
| C22×Dic32 | 3 |