Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
730 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4×D3×H(3,𝔽3) | C2 | semidirect |
| 5. #10619893 | C2 | semidirect |
| 8. C2×C3⋊#272 | C22 | semidirect |
| 9. C2×C3×#272 | C22 | semidirect |
| 12. C3×C4×H(3,𝔽3) | C22 | semidirect |
| 13. Dic3×H(3,𝔽3) | C22 | semidirect |
| 17. C32×C4×D3 | D3 | semidirect |
| 24. C4⋊#272 | D3 | direct (N × H) |
| 28. D3×H(3,𝔽3) | D4 | semidirect |
| 36. C33×C4 | C2×D3 | semidirect |
| 37. C32×Dic3 | C2×D3 | semidirect |
| 42. C2×#272 | C2×D3 | semidirect |
| 45. C4×H(3,𝔽3) | C2×D3 | semidirect |
| 46. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 67. C32×D3 | D12 | semidirect |
| 95. C32×C4 | D32 | semidirect |
| 99. C33 | C2×D12 | semidirect |
| 101. H(3,𝔽3) | D3×D4 | semidirect |
| 118. C4×D3 | #272 | semidirect |
| 155. C3×C4 | C2×#272 | semidirect |
| 157. Dic3 | C2×#272 | semidirect |
| 161. C32 | D3×D12 | semidirect |
| 183. D3 | C4⋊#272 | direct (N × H) |
| 189. C4 | D3×#272 | semidirect |
| 193. C3 | C2×C4⋊#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 |
| C4×D3×H(3,𝔽3) | 2 |
| #10619893 | 2 |
| C3×D3×D12 | 3 |
| C2×C4⋊#272 | 3 |