Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
730 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4×C3⋊#272 | C2 | semidirect |
| 3. C3×C4×#272 | C2 | semidirect |
| 4. C4×D3×H(3,𝔽3) | C2 | semidirect |
| 5. #10619890 | C2 | semidirect |
| 6. Dic3×#272 | C2 | semidirect |
| 7. D3×#1084 | C2 | semidirect |
| 13. D3×#272 | C4 | direct (N × H) |
| 14. C3×C4×H(3,𝔽3) | C22 | semidirect |
| 15. C3⋊#1084 | C22 | semidirect |
| 16. C3×#1084 | C22 | semidirect |
| 17. Dic3×H(3,𝔽3) | C22 | semidirect |
| 21. C32×C4×D3 | D3 | semidirect |
| 32. C4×#272 | D3 | direct (N × H) |
| 34. C3⋊#272 | C2×C4 | semidirect |
| 35. C3×#272 | C2×C4 | semidirect |
| 36. D3×H(3,𝔽3) | C2×C4 | semidirect |
| 44. C33×C4 | C2×D3 | semidirect |
| 47. C32×Dic3 | C2×D3 | semidirect |
| 55. C4×H(3,𝔽3) | C2×D3 | semidirect |
| 58. #1084 | C2×D3 | semidirect |
| 59. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 86. C32×D3 | C4×D3 | semidirect |
| 92. #272 | C4×D3 | direct (N × H) |
| 115. C32×C4 | D32 | semidirect |
| 126. C33 | C2×C4×D3 | semidirect |
| 128. H(3,𝔽3) | C2×C4×D3 | semidirect |
| 151. C4×D3 | #272 | direct (N × H) |
| 192. C3×C4 | C2×#272 | semidirect |
| 198. Dic3 | C2×#272 | semidirect |
| 202. C32 | C4×D32 | semidirect |
| 226. D3 | C4×#272 | direct (N × H) |
| 234. C4 | D3×#272 | direct (N × H) |
| 238. 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 |
| #10619890 | 2 |
| Dic3×#272 | 2 |
| D3×#1084 | 2 |
| C3×C4×D32 | 3 |
| C2×C4×#272 | 3 |