Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2595 conjugacy classes of subgroups; only the 499 normal subgroups are shown.
This group has 2595 conjugacy classes of subgroups — too many to draw. Only its 499 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. C23×#1084 | C2 | semidirect |
| 3. C23×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C2×#88450 | C2 | direct (N × H) |
| 10. C23×(C3⋊D3)⋊C3 | C4 | semidirect |
| 13. C22×#1084 | C22 | semidirect |
| 15. C22×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 16. #88450 | C22 | direct (N × H) |
| 19. C23×C3⋊Dic3 | D3 | semidirect |
| 33. C22×(C3⋊D3)⋊C3 | C2×C4 | semidirect |
| 36. C2×#1084 | C23 | semidirect |
| 38. C2×(C3⋊Dic3)⋊C3 | C23 | semidirect |
| 47. C23×C3⋊D3 | Dic3 | semidirect |
| 54. C22×C3⋊Dic3 | C2×D3 | semidirect |
| 65. C22×H(3,𝔽3) | C22⋊C4 | semidirect |
| 73. C2×(C3⋊D3)⋊C3 | C22×C4 | semidirect |
| 104. C22×C3⋊D3 | C2×Dic3 | semidirect |
| 112. C2×C3⋊Dic3 | C22×D3 | semidirect |
| 122. C2×H(3,𝔽3) | C2×C22⋊C4 | semidirect |
| 165. C22×C32 | (C2×D3)⋊C4 | semidirect |
| 166. C22×C32 | #217 | semidirect |
| 178. C2×C3⋊D3 | C22×Dic3 | semidirect |
| 192. H(3,𝔽3) | C22×C22⋊C4 | semidirect |
| 242. C2×C32 | C2×(C2×D3)⋊C4 | semidirect |
| 243. C2×C32 | C2×#217 | semidirect |
| 302. C32 | C22×(C2×D3)⋊C4 | semidirect |
| 303. C32 | C22×#217 | semidirect |
| 340. C22 | #88450 | direct (N × H) |
| 352. C2 | C2×#88450 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×(C3⋊D3)⋊C3 | 2 |
| C23×#1084 | 2 |
| C23×(C3⋊Dic3)⋊C3 | 2 |
| C2×#88450 | 2 |
| C22×#3722 | 3 |
| C22×(C2×D3)⋊Dic3 | 3 |