Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
801 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 801 conjugacy classes of subgroups — too many to draw. Only its 102 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×C3⋊#272 | C2 | semidirect |
| 2. C22×C3⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C2×C3×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. #10619887 | C2 | direct (N × H) |
| 10. C2×C3⋊#272 | C22 | semidirect |
| 12. C2×C3⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 13. C3×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 14. C22×C3⋊(C3⋊D3) | D3 | semidirect |
| 19. C2×C3×C3⋊Dic3 | D3 | semidirect |
| 26. C2×(C3⋊Dic3)⋊C3 | D3 | semidirect |
| 28. C2×C3×H(3,𝔽3) | D4 | semidirect |
| 41. C2×C3⋊(C3⋊D3) | C2×D3 | semidirect |
| 50. C3×C3⋊Dic3 | C2×D3 | semidirect |
| 60. (C3⋊Dic3)⋊C3 | C2×D3 | semidirect |
| 61. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 78. C2×C3⋊Dic3 | C3⋊D3 | semidirect |
| 89. C2×C33 | D12 | semidirect |
| 90. C2×C33 | #67 | semidirect |
| 100. C2×H(3,𝔽3) | D12 | semidirect |
| 151. C3⋊Dic3 | C2×C3⋊D3 | semidirect |
| 156. C33 | C2×D12 | semidirect |
| 157. C33 | C2×#67 | semidirect |
| 159. H(3,𝔽3) | C2×D12 | semidirect |
| 196. C2×C32 | #626 | semidirect |
| 197. C2×C32 | C4⋊(C3⋊D3) | semidirect |
| 259. C32 | C2×#626 | semidirect |
| 260. C32 | C2×C4⋊(C3⋊D3) | semidirect |
| 277. C2×C3 | #6200 | semidirect |
| 301. C3 | C2×#6200 | semidirect |
| 305. C2 | #10619887 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊#272 | 2 |
| C22×C3⋊((C3⋊D3)⋊C3) | 2 |
| C2×C3×(C3⋊Dic3)⋊C3 | 2 |
| #10619887 | 2 |
| C2×#6295 | 3 |
| C2×#6292 | 3 |
| C2×#6200 | 3 |