Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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. C3×C27×C31⋊C3 | C3 | semidirect |
| 3. C32⋊(C31⋊C27) | C3 | semidirect |
| 4. (C3×C31⋊C3)⋊C27 | C3 | semidirect |
| 5. C31×C32⋊C27 | C3 | semidirect |
| 14. C3×C31⋊C27 | C32 | semidirect |
| 17. C3×C27×C31 | C32 | semidirect |
| 21. C32×C31⋊C3 | C27 | semidirect |
| 42. C32×C31 | C3×C27 | semidirect |
| 49. C3×C31⋊C3 | C3×C27 | semidirect |
| 60. C32⋊C27 | C31⋊C3 | direct (N × H) |
| 66. C31⋊C3 | C32⋊C27 | direct (N × H) |
| 78. C3×C27 | C3×C31⋊C3 | semidirect |
| 79. C31 | C3×C32⋊C27 | semidirect |
| 110. C32 | C27×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C31⋊C3 | 3 |
| C3×C27×C31⋊C3 | 3 |
| C32⋊(C31⋊C27) | 3 |
| (C3×C31⋊C3)⋊C27 | 3 |
| C31×C32⋊C27 | 3 |
| C3×C32⋊C27 | 31 |