Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
318 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 318 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. C3×#14578911 | C3 | semidirect |
| 2. #21419332 | C3 | semidirect |
| 3. #21419331 | C3 | semidirect |
| 4. H(3,𝔽3)×C31⋊C9 | C3 | semidirect |
| 5. #21419213 | C3 | semidirect |
| 6. #21419213 | C3 | semidirect |
| 7. #21419209 | C3 | semidirect |
| 8. #21419207 | C3 | semidirect |
| 9. #21419207 | C3 | semidirect |
| 10. #21419203 | C3 | semidirect |
| 11. #21419203 | C3 | semidirect |
| 12. #21419203 | C3 | semidirect |
| 140. C31 | #10624595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578911 | 3 |
| #21419332 | 3 |
| #21419331 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| #21419213 | 3 |
| #21419209 | 3 |
| #21419207 | 3 |
| #21419203 | 3 |
| C31×#6856 | 3 |
| #10624595 | 31 |