Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
596 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 243 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×C8×C27 | C2 | semidirect |
| 3. C22×C27⋊C8 | C2 | semidirect |
| 4. C2×#88359 | C2 | direct (N × H) |
| 11. C2×C8×C27 | C22 | semidirect |
| 12. C2×C27⋊C8 | C22 | semidirect |
| 13. #88359 | C22 | direct (N × H) |
| 26. C8×C27 | C23 | semidirect |
| 27. C27⋊C8 | C23 | semidirect |
| 37. C22×C27 | M16 | semidirect |
| 59. C2×C27 | C2×M16 | semidirect |
| 80. C22×C8 | D27 | semidirect |
| 81. C27 | C22×M16 | semidirect |
| 102. C2×C8 | C2×D27 | semidirect |
| 120. C8 | C22×D27 | semidirect |
| 126. C22 | #88359 | direct (N × H) |
| 133. C2 | C2×#88359 | 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×C8×C27 | 2 |
| C22×C27⋊C8 | 2 |
| C2×#88359 | 2 |
| C22×#3663 | 3 |