Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
312 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 84 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. C22×C32×C27 | C2 | semidirect |
| 2. C2×C3⋊D3×C27 | C2 | semidirect |
| 3. C27×C3⋊Dic3 | C2 | semidirect |
| 13. C22×C3×C27 | D3 | semidirect |
| 16. C32×C27 | D4 | semidirect |
| 37. C22×C27 | C3⋊D3 | semidirect |
| 41. C3×C27 | #67 | semidirect |
| 42. #638 | C27 | direct (N × H) |
| 59. C22×C32 | C2×C27 | semidirect |
| 61. C2×C3⋊D3 | C2×C27 | semidirect |
| 63. C3⋊Dic3 | C2×C27 | semidirect |
| 73. C27 | #638 | direct (N × H) |
| 91. C22×C3 | D3×C27 | semidirect |
| 97. C32 | D4×C27 | semidirect |
| 111. C22 | C3⋊D3×C27 | semidirect |
| 114. C3 | #67×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C27 | 2 |
| C2×C3⋊D3×C27 | 2 |
| C27×C3⋊Dic3 | 2 |
| C9×#638 | 3 |
| #67×C27 | 3 |