Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
202 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 46 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. #21419392 | C3 | semidirect |
| 2. #21419389 | C3 | semidirect |
| 3. #21419389 | C3 | semidirect |
| 4. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 5. #21419283 | C3 | semidirect |
| 6. #21419282 | C3 | semidirect |
| 7. #21419281 | C3 | semidirect |
| 8. #21419276 | C3 | semidirect |
| 9. #21419275 | C3 | semidirect |
| 10. #21419274 | C3 | semidirect |
| 11. #21419270 | C3 | semidirect |
| 12. #21419269 | C3 | semidirect |
| 13. C31×#6881 | C3 | semidirect |
| 101. #6881 | C31⋊C3 | semidirect |
| 133. C31 | #10624850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419392 | 3 |
| #21419389 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| #21419283 | 3 |
| #21419282 | 3 |
| #21419281 | 3 |
| #21419276 | 3 |
| #21419275 | 3 |
| #21419274 | 3 |
| #21419270 | 3 |
| #21419269 | 3 |
| C31×#6881 | 3 |
| #10624850 | 31 |