Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
444 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 4. #11720139 | C2 | semidirect |
| 5. #11720137 | C2 | semidirect |
| 7. C4×Dic54 | C2 | semidirect |
| 32. C2×C4×C27 | Q8 | semidirect |
| 118. C27 | #533 | semidirect |
| 163. C2×C4 | Dic54 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×#117 | 2 |
| #11720175 | 2 |
| C2×C4×Dic27 | 2 |
| #11720139 | 2 |
| #11720137 | 2 |
| #11720127 | 2 |
| C4×Dic54 | 2 |
| #10589619 | 3 |