Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
580 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 6. #11720137 | C2 | direct (N × H) |
| 27. C2×C4×C27 | Q8 | semidirect |
| 32. C2×Dic27 | Q8 | semidirect |
| 54. C4×C27 | C2×Q8 | semidirect |
| 57. Dic27 | C2×Q8 | semidirect |
| 77. C2×C27 | C4⋊Q8 | semidirect |
| 107. C27 | C2×C4⋊Q8 | semidirect |
| 154. C2×C4 | Dic54 | semidirect |
| 169. C4 | C2×Dic54 | semidirect |
| 171. C2 | #11720137 | 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 |
| C2×C4⋊C4×C27 | 2 |
| C2×C4⋊Dic27 | 2 |
| C2×Dic27⋊C4 | 2 |
| C2×C4×Dic27 | 2 |
| #11720137 | 2 |
| C2×#63450 | 3 |