Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
476 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 112 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. #21419230 | C3 | semidirect |
| 4. #21419229 | C3 | semidirect |
| 5. C31×#6868 | C3 | semidirect |
| 12. C3×C9×C31⋊C3 | C9 | semidirect |
| 27. C3×C9×C31 | C3×C9 | semidirect |
| 31. C3×C31⋊C9 | C3×C9 | semidirect |
| 57. #6868 | C31⋊C3 | direct (N × H) |
| 64. C31⋊C3 | #6868 | direct (N × H) |
| 76. C31 | C3×#6868 | semidirect |
| 94. C3×C9 | C9×C31⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C31⋊C3 | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| #21419230 | 3 |
| #21419229 | 3 |
| C31×#6868 | 3 |
| C3×#6868 | 31 |