Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
| 5. (C31⋊C9)⋊C27 | C3 | semidirect |
| 7. #21419221 | C3 | semidirect |
| 8. #21419220 | C3 | semidirect |
| 9. C31×#6864 | C3 | semidirect |
| 38. C27×C31 | 3−1+2 | semidirect |
| 64. #6864 | C31⋊C3 | semidirect |
| 84. C31 | #10624727 | semidirect |
| 101. C27 | #11719686 | 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 |
| #21419221 | 3 |
| #21419220 | 3 |
| C31×#6864 | 3 |
| #10624727 | 31 |