Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
126 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 54 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. #10619503 | C2 | direct (N × H) |
| 3. C2×C3⋊(C9⋊C8) | C3 | semidirect |
| 11. C3⋊(C9⋊C8) | C2×C3 | semidirect |
| 13. C2×#731 | C8 | semidirect |
| 27. #731 | C2×C8 | semidirect |
| 39. C2×C3×C9 | C3×C8 | semidirect |
| 58. C3×C9 | C2×C3×C8 | semidirect |
| 101. C2 | #10619503 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#731 | 2 |
| #10619503 | 2 |
| C2×C3⋊(C9⋊C8) | 3 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 3 |