Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
172 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 76 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. #21419248 | C3 | semidirect |
| 3. #21419247 | C3 | semidirect |
| 4. (C31⋊C9)⋊C27 | C3 | semidirect |
| 5. (C31⋊C9)⋊C27 | C3 | semidirect |
| 6. (C31⋊C9)⋊C27 | C3 | semidirect |
| 10. #21419221 | C3 | semidirect |
| 11. #21419220 | C3 | semidirect |
| 12. C27×C31⋊C9 | C3 | semidirect |
| 13. C31×C9⋊C27 | C3 | semidirect |
| 74. C9⋊C27 | C31⋊C3 | semidirect |
| 103. C31 | #10624713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419294 | 3 |
| #21419248 | 3 |
| #21419247 | 3 |
| (C31⋊C9)⋊C27 | 3 |
| (C3×C31⋊C3)⋊C27 | 3 |
| #21419221 | 3 |
| #21419220 | 3 |
| C27×C31⋊C9 | 3 |
| C31×C9⋊C27 | 3 |
| #10624713 | 31 |