Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
232 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 232 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. #21419319 | C3 | semidirect |
| 2. #21419314 | C3 | semidirect |
| 3. H(3,𝔽3)×C31⋊C9 | C3 | semidirect |
| 4. #21419293 | C3 | semidirect |
| 5. #21419216 | C3 | semidirect |
| 6. #21419216 | C3 | semidirect |
| 7. #21419214 | C3 | semidirect |
| 8. #21419210 | C3 | semidirect |
| 9. #21419209 | C3 | semidirect |
| 10. #21419209 | C3 | semidirect |
| 11. #21419200 | C3 | semidirect |
| 12. #21419200 | C3 | semidirect |
| 13. C31×#6856 | C3 | semidirect |
| 104. #6856 | C31⋊C3 | semidirect |
| 138. C31 | #10624601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419319 | 3 |
| #21419314 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| #21419293 | 3 |
| #21419216 | 3 |
| #21419214 | 3 |
| #21419210 | 3 |
| #21419209 | 3 |
| #21419200 | 3 |
| C31×#6856 | 3 |
| #10624601 | 31 |