Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
1056 conjugacy classes of subgroups; only the 278 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 278 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 | direct (N × H) |
| 4. C22×#1084 | C3 | direct (N × H) |
| 5. C22×C3×H(3,𝔽3) | C4 | semidirect |
| 7. C3×#1084 | C22 | direct (N × H) |
| 12. C2×#1084 | C2×C3 | direct (N × H) |
| 13. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 18. C22×C33 | Dic3 | semidirect |
| 23. C22×H(3,𝔽3) | C3×C4 | semidirect |
| 25. #1084 | C22×C3 | direct (N × H) |
| 26. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 34. C2×C33 | C2×Dic3 | semidirect |
| 38. C2×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 47. C22×C32 | C3×Dic3 | semidirect |
| 54. C33 | C22×Dic3 | semidirect |
| 56. H(3,𝔽3) | C22×C3×C4 | semidirect |
| 68. C2×C32 | C2×C3×Dic3 | semidirect |
| 77. C22×C3 | #1084 | direct (N × H) |
| 86. C32 | C22×C3×Dic3 | semidirect |
| 94. C2×C3 | C2×#1084 | direct (N × H) |
| 98. C22 | C3×#1084 | direct (N × H) |
| 103. C3 | C22×#1084 | direct (N × H) |
| 105. C2 | C2×C3×#1084 | 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×C3×#1084 | 2 |
| C22×C32×Dic3 | 3 |
| C22×#1084 | 3 |