Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 960 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 |
|---|---|---|
| 1. C3×#14578912 | C3 | semidirect |
| 2. C3×#14578912 | C3 | semidirect |
| 3. #21419414 | C3 | semidirect |
| 4. #21419413 | C3 | semidirect |
| 5. #21419409 | C3 | semidirect |
| 6. #21419405 | C3 | semidirect |
| 7. #21419402 | C3 | semidirect |
| 8. #21419400 | C3 | semidirect |
| 9. #21419397 | C3 | semidirect |
| 10. #21419395 | C3 | semidirect |
| 11. #21419388 | C3 | semidirect |
| 12. C3×C31×#737 | C3 | semidirect |
| 24. #14578912 | C32 | semidirect |
| 25. #14578912 | C32 | semidirect |
| 26. #14578912 | C32 | semidirect |
| 32. C3×#11719686 | C32 | semidirect |
| 34. C3×#11719687 | C32 | semidirect |
| 38. C3×C9×C31⋊C3 | C32 | semidirect |
| 39. #14578901 | C32 | semidirect |
| 41. #14578898 | C32 | semidirect |
| 42. #14578896 | C32 | semidirect |
| 43. #14578895 | C32 | semidirect |
| 44. #14578893 | C32 | semidirect |
| 48. C31×#737 | C32 | semidirect |
| 49. C31×#737 | C32 | semidirect |
| 50. C31×#737 | C32 | semidirect |
| 137. C3×#737 | C31⋊C3 | semidirect |
| 171. #737 | C3×C31⋊C3 | semidirect |
| 172. #737 | C3×C31⋊C3 | semidirect |
| 173. #737 | C3×C31⋊C3 | semidirect |
| 197. C31 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| #21419414 | 3 |
| #21419413 | 3 |
| #21419409 | 3 |
| #21419405 | 3 |
| #21419402 | 3 |
| #21419400 | 3 |
| #21419397 | 3 |
| #21419395 | 3 |
| #21419388 | 3 |
| C3×C31×#737 | 3 |
| #10624929 | 31 |