Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1076 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1076 conjugacy classes of subgroups — too many to draw. Only its 382 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 |
|---|---|---|
| 3. #21419363 | C3 | direct (N × H) |
| 4. C3×#14578887 | C3 | semidirect |
| 5. C3×(C31⋊C9)⋊C9 | C3 | semidirect |
| 6. C3×C9×C31⋊C9 | C3 | semidirect |
| 7. C3×C31×C9⋊C9 | C3 | semidirect |
| 16. #14578887 | C32 | semidirect |
| 17. (C31⋊C9)⋊C9 | C32 | semidirect |
| 18. C9×C31⋊C9 | C32 | semidirect |
| 21. C31×C9⋊C9 | C32 | semidirect |
| 27. C3×C9×C31 | 3−1+2 | semidirect |
| 32. C3×C31⋊C9 | 3−1+2 | semidirect |
| 46. C9×C31 | C3×3−1+2 | semidirect |
| 49. C31⋊C9 | C3×3−1+2 | semidirect |
| 55. C3×C9⋊C9 | C31⋊C3 | semidirect |
| 57. C3×C31 | #6900 | semidirect |
| 73. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 75. C31 | C3×#6900 | semidirect |
| 89. C3×C9 | #11719686 | semidirect |
| 102. C9 | C3×#11719686 | semidirect |
| 104. C3 | #21419363 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719686 | 3 |
| #21419363 | 3 |
| C3×#14578887 | 3 |
| C3×(C31⋊C9)⋊C9 | 3 |
| C3×C9×C31⋊C9 | 3 |
| C3×C31×C9⋊C9 | 3 |
| C3×#6900 | 31 |