Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
159 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 31 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 |
|---|---|---|
| 25. C22⋊C27 | Q16 | semidirect |
| 109. C22 | Dic108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C22⋊C27)⋊Q8 | 2 |
| C8×C22⋊C27 | 2 |
| #10588788 | 3 |
| Dic108 | 4 |