Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
644 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 187 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×C4⋊C4×C27 | C2 | semidirect |
| 6. C2×Dic27⋊C4 | C2 | semidirect |
| 7. C2×Dic27⋊C4 | C2 | semidirect |
| 8. #11720145 | C2 | direct (N × H) |
| 20. C2×Dic54 | C22 | semidirect |
| 21. C4⋊C4×C27 | C22 | semidirect |
| 24. Dic27⋊C4 | C22 | semidirect |
| 25. Dic27⋊C4 | C22 | semidirect |
| 37. C22×D27 | Q8 | semidirect |
| 77. C2×D27 | C2×Q8 | semidirect |
| 112. C2×C27 | C22⋊Q8 | semidirect |
| 152. C2×C4⋊C4 | D27 | semidirect |
| 155. C27 | C2×C22⋊Q8 | semidirect |
| 193. C4⋊C4 | C2×D27 | semidirect |
| 251. C2 | #11720145 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D27 | 2 |
| C22×Dic54 | 2 |
| C2×C4⋊C4×C27 | 2 |
| C2×(C2×D27)⋊C4 | 2 |
| C2×Dic27⋊C4 | 2 |
| #11720145 | 2 |
| C2×#63458 | 3 |