Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
220 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #21419247 | C3 | semidirect |
| 4. (C31⋊C9)⋊C27 | C3 | semidirect |
| 6. C27×C31⋊C9 | C3 | semidirect |
| 7. C9×C27×C31 | C3 | semidirect |
| 27. #11719686 | C27 | direct (N × H) |
| 31. C27×C31 | 3−1+2 | semidirect |
| 40. C9×C31 | C3×C27 | semidirect |
| 45. C31⋊C9 | C3×C27 | semidirect |
| 52. C9×C27 | C31⋊C3 | semidirect |
| 69. C31 | C27×3−1+2 | semidirect |
| 83. C27 | #11719686 | direct (N × H) |
| 92. C9 | C27×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C27×C31⋊C3 | 3 |
| C9×#11719686 | 3 |
| #21419247 | 3 |
| (C31⋊C9)⋊C27 | 3 |
| (C3×C31⋊C3)⋊C27 | 3 |
| C27×C31⋊C9 | 3 |
| C9×C27×C31 | 3 |
| C27×3−1+2 | 31 |