Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
596 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 596 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. C22×C8×C27 | C2 | semidirect |
| 4. C2×#88360 | C2 | direct (N × H) |
| 12. C2×Dic54 | C22 | semidirect |
| 13. C2×C8×C27 | C22 | semidirect |
| 14. #88360 | C22 | direct (N × H) |
| 28. Dic54 | C23 | semidirect |
| 29. C8×C27 | C23 | semidirect |
| 40. C22×C27 | SD16 | semidirect |
| 63. C2×C27 | C2×SD16 | semidirect |
| 85. C22×C8 | D27 | semidirect |
| 86. C27 | C22×SD16 | semidirect |
| 109. C2×C8 | C2×D27 | semidirect |
| 128. C8 | C22×D27 | semidirect |
| 134. C22 | #88360 | direct (N × H) |
| 141. C2 | C2×#88360 | 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 |
| C22×C8×C27 | 2 |
| C2×#88360 | 2 |
| C22×#3664 | 3 |