Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 171 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×M16×C27 | C2 | semidirect |
| 4. #11720158 | C2 | direct (N × H) |
| 5. C2×#88360 | C2 | semidirect |
| 6. C2×Dic108 | C2 | semidirect |
| 19. C2×Dic54 | C22 | semidirect |
| 20. M16×C27 | C22 | semidirect |
| 22. #88360 | C22 | semidirect |
| 23. Dic108 | C22 | semidirect |
| 103. C2×C27 | #137 | semidirect |
| 137. C2×M16 | D27 | semidirect |
| 138. C27 | C2×#137 | semidirect |
| 176. M16 | C2×D27 | semidirect |
| 225. C2 | #11720158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88399 | 2 |
| C22×Dic54 | 2 |
| C2×M16×C27 | 2 |
| #11720158 | 2 |
| C2×#88360 | 2 |
| C2×Dic108 | 2 |
| C2×#63471 | 3 |