Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
826 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×C3×#1084 | C2 | semidirect |
| 3. C2×Dic3×H(3,𝔽3) | C2 | semidirect |
| 4. #10619890 | C2 | direct (N × H) |
| 8. C2×C3⋊#272 | C4 | semidirect |
| 10. C3×#1084 | C22 | semidirect |
| 11. Dic3×H(3,𝔽3) | C22 | semidirect |
| 14. C2×C32×Dic3 | D3 | semidirect |
| 19. C2×#1084 | D3 | semidirect |
| 21. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 23. C3⋊#272 | C2×C4 | semidirect |
| 31. C32×Dic3 | C2×D3 | semidirect |
| 39. #1084 | C2×D3 | semidirect |
| 40. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 55. C2×C33 | C4×D3 | semidirect |
| 60. C2×H(3,𝔽3) | C4×D3 | semidirect |
| 87. C33 | C2×C4×D3 | semidirect |
| 89. H(3,𝔽3) | C2×C4×D3 | semidirect |
| 101. C2×Dic3 | #272 | semidirect |
| 110. C2×C32 | #624 | semidirect |
| 138. Dic3 | C2×#272 | semidirect |
| 142. C32 | C2×#624 | semidirect |
| 155. C2×C3 | C4×#272 | semidirect |
| 170. C3 | C2×C4×#272 | semidirect |
| 173. C2 | #10619890 | 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 |
| C2×C3×#1084 | 2 |
| C2×Dic3×H(3,𝔽3) | 2 |
| #10619890 | 2 |
| C2×C3×#624 | 3 |
| C2×C4×#272 | 3 |