Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
322 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 77 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⋊C8×H(3,𝔽3) | C2 | semidirect |
| 4. C32×#215 | C3 | semidirect |
| 9. C33×Q8 | C2×C3 | semidirect |
| 11. C32×C3⋊C8 | C2×C3 | semidirect |
| 13. Q8×H(3,𝔽3) | D3 | semidirect |
| 29. C3×H(3,𝔽3) | SD16 | semidirect |
| 33. C32×Q8 | C3×D3 | semidirect |
| 48. #215 | H(3,𝔽3) | direct (N × H) |
| 62. C33 | C3×SD16 | semidirect |
| 64. H(3,𝔽3) | #215 | direct (N × H) |
| 68. C3×Q8 | C2×H(3,𝔽3) | semidirect |
| 75. C3⋊C8 | C2×H(3,𝔽3) | semidirect |
| 101. C32 | C3×#215 | semidirect |
| 103. Q8 | D3×H(3,𝔽3) | semidirect |
| 120. C3 | SD16×H(3,𝔽3) | semidirect |
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 |
| D12×H(3,𝔽3) | 2 |
| C3⋊C8×H(3,𝔽3) | 2 |
| C32×#215 | 3 |
| SD16×H(3,𝔽3) | 3 |