Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
400 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 44. Dic54 | Q8 | semidirect |
| 127. C27 | #557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×C4⋊Q8 | 2 |
| Q8×Dic27 | 2 |
| #11720193 | 2 |
| #11720139 | 2 |
| #11720138 | 2 |
| #11720136 | 2 |
| C4×Dic54 | 2 |
| #10589823 | 3 |