Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
218 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 1. #21419329 | C3 | semidirect |
| 2. #21419322 | C3 | semidirect |
| 3. C9×#11719689 | C3 | semidirect |
| 4. #21419213 | C3 | semidirect |
| 5. #21419213 | C3 | semidirect |
| 6. #21419210 | C3 | semidirect |
| 7. #21419206 | C3 | semidirect |
| 8. #21419206 | C3 | semidirect |
| 9. #21419204 | C3 | semidirect |
| 10. #21419203 | C3 | semidirect |
| 11. #21419203 | C3 | semidirect |
| 13. C9×H(3,𝔽3)×C31 | C3 | semidirect |
| 93. C9×H(3,𝔽3) | C31⋊C3 | semidirect |
| 135. C31 | #10624623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419329 | 3 |
| #21419322 | 3 |
| C9×#11719689 | 3 |
| #21419213 | 3 |
| #21419210 | 3 |
| #21419206 | 3 |
| #21419204 | 3 |
| #21419203 | 3 |
| #21419200 | 3 |
| C9×H(3,𝔽3)×C31 | 3 |
| #10624623 | 31 |