Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
660 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 660 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 |
|---|---|---|
| 2. C22×Dic54 | C2 | semidirect |
| 3. C2×C42×C27 | C2 | semidirect |
| 4. C2×(C2×D27)⋊C4 | C2 | semidirect |
| 5. #11720124 | C2 | direct (N × H) |
| 14. C2×Dic54 | C22 | semidirect |
| 15. C42×C27 | C22 | semidirect |
| 16. (C2×D27)⋊C4 | C22 | semidirect |
| 72. C2×C27 | #124 | semidirect |
| 99. C2×C42 | D27 | semidirect |
| 100. C27 | C2×#124 | semidirect |
| 126. C42 | C2×D27 | semidirect |
| 164. C2 | #11720124 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D108 | 2 |
| C22×Dic54 | 2 |
| C2×C42×C27 | 2 |
| C2×(C2×D27)⋊C4 | 2 |
| #11720124 | 2 |
| C2×#63437 | 3 |