Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3351 conjugacy classes of subgroups; only the 595 normal subgroups are shown.
This group has 3351 conjugacy classes of subgroups — too many to draw. Only its 595 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 |
|---|---|---|
| 1. C22×C4×#272 | C2 | semidirect |
| 2. C22×C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. C22×#6200 | C2 | semidirect |
| 4. C22×#6198 | C2 | semidirect |
| 5. C22×#6196 | C2 | semidirect |
| 6. C2×#88650 | C2 | direct (N × H) |
| 12. C2×C4×#272 | C22 | semidirect |
| 14. C2×C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 15. C2×#6200 | C22 | semidirect |
| 16. C2×#6198 | C22 | semidirect |
| 17. C2×#6196 | C22 | semidirect |
| 18. #88650 | C22 | direct (N × H) |
| 19. C22×C4×C3⋊D3 | D3 | semidirect |
| 35. C4×#272 | C23 | semidirect |
| 37. C4×(C3⋊D3)⋊C3 | C23 | semidirect |
| 38. #6200 | C23 | semidirect |
| 39. #6198 | C23 | semidirect |
| 40. #6196 | C23 | semidirect |
| 50. C2×C4×C3⋊D3 | C2×D3 | semidirect |
| 62. C22×H(3,𝔽3) | #41 | semidirect |
| 99. C4×C3⋊D3 | C22×D3 | semidirect |
| 111. C2×H(3,𝔽3) | C2×#41 | semidirect |
| 147. C22×C32 | #235 | semidirect |
| 169. H(3,𝔽3) | C22×#41 | semidirect |
| 209. C2×C32 | C2×#235 | semidirect |
| 254. C32 | C22×#235 | semidirect |
| 284. C22 | #88650 | direct (N × H) |
| 294. C2 | C2×#88650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#272 | 2 |
| C22×C4×(C3⋊D3)⋊C3 | 2 |
| C22×#6200 | 2 |
| C22×#6198 | 2 |
| C22×#6196 | 2 |
| C2×#88650 | 2 |
| C22×#3798 | 3 |