Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
282 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 118 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. C3×(C27⋊C3)⋊C4 | C2 | direct (N × H) |
| 4. C2×(C27⋊C3)⋊C4 | C3 | direct (N × H) |
| 5. C2×C3×Dic27 | C3 | semidirect |
| 6. C2×C3×C27⋊C3 | C4 | semidirect |
| 14. (C27⋊C3)⋊C4 | C2×C3 | direct (N × H) |
| 15. C3×Dic27 | C2×C3 | semidirect |
| 16. C3×C27⋊C3 | C2×C4 | semidirect |
| 20. C2×Dic27 | C32 | semidirect |
| 25. C2×C27⋊C3 | C3×C4 | semidirect |
| 29. C2×C3×C27 | C3×C4 | semidirect |
| 42. Dic27 | C2×C32 | semidirect |
| 45. C27⋊C3 | C2×C3×C4 | semidirect |
| 47. C3×C27 | C2×C3×C4 | semidirect |
| 66. C2×C27 | C32×C4 | semidirect |
| 86. C27 | C2×C32×C4 | semidirect |
| 123. C2×C3 | (C27⋊C3)⋊C4 | direct (N × H) |
| 131. C3 | C2×(C27⋊C3)⋊C4 | direct (N × H) |
| 133. C2 | C3×(C27⋊C3)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C27⋊C3 | 2 |
| C3×(C27⋊C3)⋊C4 | 2 |
| C2×C32×Dic9 | 3 |
| C2×(C27⋊C3)⋊C4 | 3 |
| C2×C3×Dic27 | 3 |