Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
866 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 301 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×Dic3×H(3,𝔽3) | C2 | direct (N × H) |
| 3. C22×C32×Dic3 | C3 | semidirect |
| 5. C22×C3×H(3,𝔽3) | C4 | semidirect |
| 7. Dic3×H(3,𝔽3) | C22 | direct (N × H) |
| 9. C2×C32×Dic3 | C2×C3 | semidirect |
| 13. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 18. C22×C33 | C3×C4 | semidirect |
| 20. C32×Dic3 | C22×C3 | semidirect |
| 23. C22×H(3,𝔽3) | Dic3 | direct (N × H) |
| 26. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 35. C2×C33 | C2×C3×C4 | semidirect |
| 39. C2×H(3,𝔽3) | C2×Dic3 | direct (N × H) |
| 43. C22×Dic3 | H(3,𝔽3) | direct (N × H) |
| 50. C22×C32 | C3×Dic3 | semidirect |
| 57. C33 | C22×C3×C4 | semidirect |
| 59. H(3,𝔽3) | C22×Dic3 | direct (N × H) |
| 67. C2×Dic3 | C2×H(3,𝔽3) | direct (N × H) |
| 74. C2×C32 | C2×C3×Dic3 | semidirect |
| 85. C22×C3 | C4×H(3,𝔽3) | semidirect |
| 91. Dic3 | C22×H(3,𝔽3) | direct (N × H) |
| 95. C32 | C22×C3×Dic3 | semidirect |
| 105. C2×C3 | C2×C4×H(3,𝔽3) | semidirect |
| 109. C22 | Dic3×H(3,𝔽3) | direct (N × H) |
| 115. C3 | C22×C4×H(3,𝔽3) | semidirect |
| 117. C2 | C2×Dic3×H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×H(3,𝔽3) | 2 |
| C2×Dic3×H(3,𝔽3) | 2 |
| C22×C32×Dic3 | 3 |
| C22×C4×H(3,𝔽3) | 3 |