Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1076 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1076 conjugacy classes of subgroups — too many to draw. Only its 355 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. #21419363 | C3 | semidirect |
| 3. #21419362 | C3 | semidirect |
| 4. #21419361 | C3 | semidirect |
| 5. #21419360 | C3 | semidirect |
| 6. #21419359 | C3 | semidirect |
| 7. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 8. C92×C31⋊C3 | C3 | semidirect |
| 9. C31×#6900 | C3 | semidirect |
| 19. #14578887 | C32 | semidirect |
| 20. #14578886 | C32 | semidirect |
| 21. (C31⋊C9)⋊C9 | C32 | semidirect |
| 22. C9×C31⋊C9 | C32 | semidirect |
| 24. C31×C9⋊C9 | C32 | semidirect |
| 25. C92×C31 | C32 | semidirect |
| 43. C9×C31⋊C3 | 3−1+2 | semidirect |
| 52. C9×C31 | C3×3−1+2 | semidirect |
| 55. C31⋊C9 | C3×3−1+2 | semidirect |
| 62. #6900 | C31⋊C3 | direct (N × H) |
| 69. C31⋊C3 | #6900 | direct (N × H) |
| 83. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 85. C92 | C3×C31⋊C3 | semidirect |
| 86. C31 | C3×#6900 | semidirect |
| 115. C9 | 3−1+2×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C31⋊C3 | 3 |
| #21419363 | 3 |
| #21419362 | 3 |
| #21419361 | 3 |
| #21419360 | 3 |
| #21419359 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| C92×C31⋊C3 | 3 |
| C31×#6900 | 3 |
| C3×#6900 | 31 |