Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
758 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 286 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 |
|---|---|---|
| 2. #21419359 | C3 | semidirect |
| 3. #21419351 | C3 | semidirect |
| 4. #21419338 | C3 | semidirect |
| 5. #21419337 | C3 | semidirect |
| 6. #21419332 | C3 | semidirect |
| 7. #21419331 | C3 | semidirect |
| 8. #21419330 | C3 | semidirect |
| 9. #21419329 | C3 | semidirect |
| 11. #21419306 | C3 | semidirect |
| 12. 3−1+2×C31⋊C9 | C3 | semidirect |
| 13. #21419293 | C3 | semidirect |
| 14. C3×C9×C31⋊C9 | C3 | semidirect |
| 68. C3×C31⋊C9 | 3−1+2 | semidirect |
| 89. C9×C31 | #737 | semidirect |
| 99. C31⋊C9 | #737 | semidirect |
| 157. C31 | #10624879 | semidirect |
| 203. C9 | #14578911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578911 | 3 |
| #21419359 | 3 |
| #21419351 | 3 |
| #21419338 | 3 |
| #21419337 | 3 |
| #21419332 | 3 |
| #21419331 | 3 |
| #21419330 | 3 |
| #21419329 | 3 |
| #21419314 | 3 |
| #21419306 | 3 |
| 3−1+2×C31⋊C9 | 3 |
| #21419293 | 3 |
| C3×C9×C31⋊C9 | 3 |
| C31×C9⋊H(3,𝔽3) | 3 |
| #10624879 | 31 |