Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
645 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 645 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×C4×#272 | C2 | semidirect |
| 3. C4×C3⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 4. #10619903 | C2 | semidirect |
| 5. #10619901 | C2 | semidirect |
| 10. #66432 | C4 | direct (N × H) |
| 11. C3×C4×H(3,𝔽3) | C22 | semidirect |
| 12. C3×#1084 | C22 | semidirect |
| 13. C3⋊((C3⋊Dic3)⋊C3) | C22 | semidirect |
| 15. C4×C3⋊(C3⋊D3) | D3 | semidirect |
| 23. C4×#272 | D3 | semidirect |
| 29. C3×#272 | C2×C4 | semidirect |
| 30. C3⋊((C3⋊D3)⋊C3) | C2×C4 | semidirect |
| 40. C33×C4 | C2×D3 | semidirect |
| 41. C3⋊(C3⋊Dic3) | C2×D3 | semidirect |
| 51. C4×H(3,𝔽3) | C2×D3 | semidirect |
| 52. #1084 | C2×D3 | semidirect |
| 55. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 80. C3⋊(C3⋊D3) | C4×D3 | semidirect |
| 87. #272 | C4×D3 | semidirect |
| 114. C32×C4 | D32 | semidirect |
| 126. C33 | C2×C4×D3 | semidirect |
| 129. H(3,𝔽3) | C2×C4×D3 | semidirect |
| 187. C3×C4 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 201. C32 | C4×D32 | semidirect |
| 227. C4 | #66432 | direct (N × H) |
| 232. C3 | C4×((C3⋊D3)⋊C3)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66432 | 2 |
| C3×C4×#272 | 2 |
| C4×C3⋊((C3⋊D3)⋊C3) | 2 |
| #10619903 | 2 |
| #10619901 | 2 |
| C4×D3×C3⋊D3 | 3 |
| C4×((C3⋊D3)⋊C3)⋊C2 | 3 |