Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
340 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 76 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. C32⋊(C22⋊C27) | C2 | direct (N × H) |
| 3. C2×C3×C22⋊C27 | C3 | semidirect |
| 8. C3×C22⋊C27 | C2×C3 | semidirect |
| 40. C23×C32 | C27 | semidirect |
| 71. C22×C32 | C2×C27 | semidirect |
| 102. C2×C32 | C22⋊C27 | semidirect |
| 127. C32 | C2×C22⋊C27 | semidirect |
| 132. C23 | C32⋊C27 | semidirect |
| 147. C22 | C2×C32⋊C27 | semidirect |
| 154. C2 | C32⋊(C22⋊C27) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32⋊(C22⋊C27) | 2 |
| C23×C32×C9 | 3 |
| C2×C3×C22⋊C27 | 3 |
| C2×C32⋊C27 | 4 |