Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
730 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×D3×#272 | C2 | semidirect |
| 2. C4⋊(C3⋊#272) | C2 | semidirect |
| 3. C3×C4×#272 | C2 | semidirect |
| 4. D12×H(3,𝔽3) | C2 | semidirect |
| 5. #10619892 | C2 | semidirect |
| 8. C2×C3⋊#272 | C22 | semidirect |
| 10. C2×D3×H(3,𝔽3) | C22 | semidirect |
| 12. C3×C4×H(3,𝔽3) | C22 | semidirect |
| 13. C3×#1084 | C22 | semidirect |
| 16. C32×D12 | D3 | semidirect |
| 24. C4×#272 | D3 | semidirect |
| 27. C3×#272 | D4 | semidirect |
| 34. C2×C32×D3 | C2×D3 | semidirect |
| 36. C33×C4 | C2×D3 | semidirect |
| 44. C4×H(3,𝔽3) | C2×D3 | semidirect |
| 45. #1084 | C2×D3 | semidirect |
| 46. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 73. #272 | D12 | direct (N × H) |
| 95. C32×C4 | D32 | semidirect |
| 100. C33 | D3×D4 | semidirect |
| 102. H(3,𝔽3) | C2×D12 | semidirect |
| 118. D12 | #272 | direct (N × H) |
| 150. C2×D3 | C2×#272 | semidirect |
| 157. C3×C4 | C2×#272 | semidirect |
| 163. C32 | D3×D12 | semidirect |
| 191. C4 | D3×#272 | semidirect |
| 195. C3 | D4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#272 | 2 |
| C4⋊(C3⋊#272) | 2 |
| C3×C4×#272 | 2 |
| D12×H(3,𝔽3) | 2 |
| #10619892 | 2 |
| C3×D3×D12 | 3 |
| D4×#272 | 3 |