Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
488 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 162 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. C3×Q8×H(3,𝔽3) | C2 | semidirect |
| 3. C3×#634⋊C3 | C2 | semidirect |
| 4. C3×Q8×C3⋊D3 | C3 | semidirect |
| 6. Q8×(C3⋊D3)⋊C3 | C3 | direct (N × H) |
| 11. C33×Q8 | D3 | semidirect |
| 12. C33×Q8 | C2×C3 | semidirect |
| 14. C3×#634 | C2×C3 | semidirect |
| 18. Q8×H(3,𝔽3) | C2×C3 | semidirect |
| 20. #634⋊C3 | C2×C3 | semidirect |
| 22. C3×(C3⋊D3)⋊C3 | Q8 | direct (N × H) |
| 24. Q8×C3⋊D3 | C32 | semidirect |
| 39. C3×H(3,𝔽3) | C2×Q8 | semidirect |
| 50. C32×Q8 | C3×D3 | semidirect |
| 51. C32×Q8 | C2×C32 | semidirect |
| 54. #634 | C2×C32 | semidirect |
| 64. C3×C3⋊D3 | C3×Q8 | semidirect |
| 68. (C3⋊D3)⋊C3 | C3×Q8 | direct (N × H) |
| 95. C33 | D3×Q8 | semidirect |
| 96. C33 | C2×C3×Q8 | semidirect |
| 98. H(3,𝔽3) | C2×C3×Q8 | semidirect |
| 106. C3×Q8 | (C3⋊D3)⋊C3 | direct (N × H) |
| 126. C3⋊D3 | C32×Q8 | semidirect |
| 155. C32 | C3×D3×Q8 | semidirect |
| 156. C32 | C2×C32×Q8 | semidirect |
| 158. Q8 | C3×(C3⋊D3)⋊C3 | direct (N × H) |
| 179. C3 | Q8×(C3⋊D3)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×H(3,𝔽3) | 2 |
| C3×C4×(C3⋊D3)⋊C3 | 2 |
| C3×#634⋊C3 | 2 |
| C3×Q8×C3⋊D3 | 3 |
| C32×D3×Q8 | 3 |
| Q8×(C3⋊D3)⋊C3 | 3 |