Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1064 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 271 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. #737×C31⋊C3 | C3 | semidirect |
| 2. C32×C9×C31⋊C3 | C3 | semidirect |
| 3. #21419392 | C3 | semidirect |
| 4. #21419391 | C3 | semidirect |
| 5. #21419390 | C3 | semidirect |
| 6. #21419389 | C3 | semidirect |
| 7. #21419388 | C3 | semidirect |
| 8. #21419387 | C3 | semidirect |
| 9. #733×C31⋊C3 | C3 | semidirect |
| 10. #732×C31⋊C3 | C3 | semidirect |
| 11. #731×C31⋊C3 | C3 | semidirect |
| 12. AΣL(1,𝔽27)×C31⋊C3 | C3 | semidirect |
| 13. C31×#6908 | C3 | semidirect |
| 16. #14578913 | C32 | semidirect |
| 18. #14578912 | C32 | semidirect |
| 19. #14578911 | C32 | semidirect |
| 23. C32×C31⋊C9 | C32 | semidirect |
| 32. C3×C9×C31⋊C3 | C32 | semidirect |
| 33. C3×C9×C31⋊C3 | C32 | semidirect |
| 34. C3×C9×C31⋊C3 | C32 | semidirect |
| 35. #14578902 | C32 | semidirect |
| 36. #14578901 | C32 | semidirect |
| 37. #14578900 | C32 | semidirect |
| 38. #14578899 | C32 | semidirect |
| 39. #14578898 | C32 | semidirect |
| 40. #14578897 | C32 | semidirect |
| 41. #14578896 | C32 | semidirect |
| 42. #14578895 | C32 | semidirect |
| 43. #14578894 | C32 | semidirect |
| 44. #14578893 | C32 | semidirect |
| 45. C31×#737 | C32 | semidirect |
| 46. C32×C9×C31 | C32 | semidirect |
| 47. C31×#733 | C32 | semidirect |
| 48. C31×#732 | C32 | semidirect |
| 49. C31×#731 | C32 | semidirect |
| 50. C31×AΣL(1,𝔽27) | C32 | semidirect |
| 132. #6908 | C31⋊C3 | direct (N × H) |
| 144. C31⋊C3 | #6908 | direct (N × H) |
| 151. #737 | C3×C31⋊C3 | semidirect |
| 167. C32×C9 | C3×C31⋊C3 | semidirect |
| 170. #733 | C3×C31⋊C3 | semidirect |
| 173. #732 | C3×C31⋊C3 | semidirect |
| 177. #731 | C3×C31⋊C3 | semidirect |
| 181. AΣL(1,𝔽27) | C3×C31⋊C3 | semidirect |
| 182. C31 | C3×#6908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #737×C31⋊C3 | 3 |
| C32×C9×C31⋊C3 | 3 |
| #21419392 | 3 |
| #21419391 | 3 |
| #21419390 | 3 |
| #21419389 | 3 |
| #21419388 | 3 |
| #21419387 | 3 |
| #733×C31⋊C3 | 3 |
| #732×C31⋊C3 | 3 |
| #731×C31⋊C3 | 3 |
| AΣL(1,𝔽27)×C31⋊C3 | 3 |
| C31×#6908 | 3 |
| C3×#6908 | 31 |