Finite Group DatabasebetaFinite Group DatabasebetaOrder 3888.
356 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. C22×AGL(1,ℤ/27) | C2 | semidirect |
| 2. C2×C4×#6875 | C2 | semidirect |
| 3. C4⋊AGL(1,ℤ/27) | C2 | direct (N × H) |
| 8. C2×AGL(1,ℤ/27) | C22 | semidirect |
| 9. C4×#6875 | C22 | semidirect |
| 17. C2×#6875 | D4 | semidirect |
| 22. C2×D108 | C9 | semidirect |
| 33. #6875 | C2×D4 | semidirect |
| 40. C22×D27 | C2×C9 | semidirect |
| 43. C2×C4×C27 | C2×C9 | semidirect |
| 44. D108 | C2×C9 | semidirect |
| 68. C2×D27 | C22×C9 | semidirect |
| 71. C4×C27 | C22×C9 | semidirect |
| 95. C2×C27 | D4×C9 | semidirect |
| 118. C27 | C2×D4×C9 | semidirect |
| 151. C2×C4 | AGL(1,ℤ/27) | semidirect |
| 161. C4 | C2×AGL(1,ℤ/27) | semidirect |
| 165. C2 | C4⋊AGL(1,ℤ/27) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×AGL(1,ℤ/27) | 2 |
| C2×C4×#6875 | 2 |
| C4⋊AGL(1,ℤ/27) | 2 |
| C2×C4⋊(D27⋊C3) | 3 |
| C2×C4⋊(D9⋊C9) | 3 |