Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
196 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 82 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. #21419248 | C3 | semidirect |
| 4. (C31⋊C9)⋊C27 | C3 | semidirect |
| 5. (C31⋊C9)⋊C27 | C3 | semidirect |
| 6. (C31⋊C9)⋊C27 | C3 | semidirect |
| 7. (C31⋊C9)⋊C27 | C3 | semidirect |
| 10. #21419222 | C3 | semidirect |
| 11. #21419221 | C3 | semidirect |
| 12. #21419220 | C3 | semidirect |
| 13. C31×C9⋊C27 | C3 | semidirect |
| 62. C31⋊C27 | 3−1+2 | semidirect |
| 90. C9⋊C27 | C31⋊C3 | semidirect |
| 124. C31 | #10624727 | 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 |
| #21419248 | 3 |
| (C31⋊C9)⋊C27 | 3 |
| (C3×C31⋊C3)⋊C27 | 3 |
| #21419222 | 3 |
| #21419221 | 3 |
| #21419220 | 3 |
| C31×C9⋊C27 | 3 |
| #10624727 | 31 |