Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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. #21419326 | C3 | semidirect |
| 2. #21419323 | C3 | semidirect |
| 3. #21419306 | C3 | semidirect |
| 4. H(3,𝔽3)×C31⋊C9 | C3 | semidirect |
| 5. #21419212 | C3 | semidirect |
| 6. #21419212 | C3 | semidirect |
| 7. #21419211 | C3 | semidirect |
| 8. #21419208 | C3 | semidirect |
| 9. #21419205 | C3 | semidirect |
| 10. #21419203 | C3 | semidirect |
| 11. #21419202 | C3 | semidirect |
| 13. C31×#6857 | C3 | semidirect |
| 101. #6857 | 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 |
|---|---|
| #21419326 | 3 |
| #21419323 | 3 |
| #21419306 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| #21419212 | 3 |
| #21419211 | 3 |
| #21419208 | 3 |
| #21419205 | 3 |
| #21419203 | 3 |
| #21419202 | 3 |
| #21419200 | 3 |
| C31×#6857 | 3 |
| #10624623 | 31 |