Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 3. C2×Dic108 | C2 | direct (N × H) |
| 10. Dic108 | C22 | direct (N × H) |
| 28. C22×C27 | Q16 | semidirect |
| 44. C2×C27 | C2×Q16 | semidirect |
| 60. C27 | C22×Q16 | semidirect |
| 91. C22 | Dic108 | direct (N × H) |
| 97. C2 | C2×Dic108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic54 | 2 |
| C22×C8×C27 | 2 |
| C2×Dic108 | 2 |
| C22×Dic36 | 3 |