Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×Q8⋊C27 | C2 | semidirect |
| 4. #41⋊C27 | C4 | semidirect |
| 14. Q8⋊C27 | C2×C4 | semidirect |
| 47. #520 | C27 | semidirect |
| 94. #41 | C4×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41⋊C27 | 2 |
| C4×Q8⋊C27 | 2 |
| C9×#520 | 3 |
| C4⋊C4×C27 | 4 |