Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
200 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 58 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. #21419330 | C3 | semidirect |
| 2. C9×#11719689 | C3 | semidirect |
| 3. #21419296 | C3 | semidirect |
| 4. C31⋊#6862 | C3 | semidirect |
| 5. #21419214 | C3 | semidirect |
| 8. #21419208 | C3 | semidirect |
| 9. #21419208 | C3 | semidirect |
| 10. #21419207 | C3 | semidirect |
| 11. #21419207 | C3 | semidirect |
| 128. C31 | #10624621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419330 | 3 |
| C9×#11719689 | 3 |
| #21419296 | 3 |
| C31⋊#6862 | 3 |
| #21419214 | 3 |
| #21419209 | 3 |
| #21419208 | 3 |
| #21419207 | 3 |
| #21419203 | 3 |
| C31×C9⋊H(3,𝔽3) | 3 |
| #10624621 | 31 |