Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
292 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 100 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. 3−1+2×C31⋊C9 | C3 | semidirect |
| 3. C3×C9×C31⋊C9 | C3 | semidirect |
| 4. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 6. #21419228 | C3 | semidirect |
| 22. C31×#731 | C9 | semidirect |
| 26. 3−1+2×C31 | C3×C9 | semidirect |
| 32. C3×C9×C31 | C3×C9 | semidirect |
| 56. C31⋊C9 | #731 | direct (N × H) |
| 76. #731 | C31⋊C9 | direct (N × H) |
| 85. C31 | C9×#731 | semidirect |
| 89. 3−1+2 | C3×C31⋊C9 | semidirect |
| 103. C3×C9 | C3×C31⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×C31⋊C9 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| C3×C9×C31⋊C9 | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| H(3,𝔽3)⋊(C31⋊C9) | 3 |
| #21419228 | 3 |
| C3×C31×#731 | 3 |
| C9×#731 | 31 |