Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
378 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 123 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. C23×C3×C27 | C2 | semidirect |
| 2. C22×C3⋊D27 | C2 | semidirect |
| 3. #10619677 | C2 | direct (N × H) |
| 4. C2×C3⋊Dic27 | C2 | semidirect |
| 9. C22×C3×C27 | C22 | semidirect |
| 11. C2×C3⋊D27 | C22 | semidirect |
| 12. C3⋊Dic27 | C22 | semidirect |
| 17. C23×C27 | D3 | semidirect |
| 22. C2×C3×C27 | D4 | semidirect |
| 36. C22×C27 | C2×D3 | semidirect |
| 40. C3×C27 | C2×D4 | semidirect |
| 58. C2×C27 | #67 | semidirect |
| 82. C27 | C2×#67 | semidirect |
| 83. C23×C3 | D27 | semidirect |
| 107. C22×C3 | C2×D27 | semidirect |
| 120. C23 | C3⋊D27 | semidirect |
| 125. C2×C3 | #6171 | semidirect |
| 135. C22 | C2×C3⋊D27 | semidirect |
| 137. C3 | C2×#6171 | semidirect |
| 141. C2 | #10619677 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C27 | 2 |
| C22×C3⋊D27 | 2 |
| #10619677 | 2 |
| C2×C3⋊Dic27 | 2 |
| C2×#6233 | 3 |
| C2×#6171 | 3 |