Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
264 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11757622 | C2 | direct (N × H) |
| 4. C2×C3⋊Dic27 | C3 | semidirect |
| 7. C2×#6903 | C4 | semidirect |
| 17. C3⋊Dic27 | C2×C3 | semidirect |
| 20. #6903 | C2×C4 | semidirect |
| 33. C2×C27⋊C3 | Dic3 | semidirect |
| 37. C2×C3×C27 | Dic3 | semidirect |
| 38. C2×C3×C27 | C3×C4 | semidirect |
| 61. C27⋊C3 | C2×Dic3 | semidirect |
| 63. C3×C27 | C2×Dic3 | semidirect |
| 64. C3×C27 | C2×C3×C4 | semidirect |
| 159. C2 | #11757622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6903 | 2 |
| #11757622 | 2 |
| C2×#66409 | 3 |
| C2×C3⋊Dic27 | 3 |
| C2×(C27⋊C3)⋊C4 | 3 |
| C2×C3×Dic27 | 3 |