Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 224 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. #21419370 | C3 | semidirect |
| 3. C3×C27×C31⋊C3 | C3 | semidirect |
| 4. #21419244 | C3 | semidirect |
| 5. #21419243 | C3 | semidirect |
| 6. #21419241 | C3 | semidirect |
| 7. #21419240 | C3 | semidirect |
| 8. #21419231 | C3 | semidirect |
| 9. C31×#6903 | C3 | semidirect |
| 70. #6903 | C31⋊C3 | semidirect |
| 104. C31 | #10624724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419388 | 3 |
| #21419370 | 3 |
| C3×C27×C31⋊C3 | 3 |
| #21419244 | 3 |
| #21419243 | 3 |
| #21419241 | 3 |
| #21419240 | 3 |
| #21419231 | 3 |
| C31×#6903 | 3 |
| #10624724 | 31 |