Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1988 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 1988 conjugacy classes of subgroups — too many to draw. Only its 166 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. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 2. #21419226 | C3 | direct (N × H) |
| 6. C32⋊(C31⋊C9) | C32 | semidirect |
| 11. C34×C31 | C9 | semidirect |
| 25. C33×C31 | C3×C9 | semidirect |
| 57. C3×C31 | #6866 | semidirect |
| 64. C34 | C31⋊C9 | semidirect |
| 70. C31 | C3×#6866 | semidirect |
| 82. C33 | C3×C31⋊C9 | semidirect |
| 110. C3 | #21419226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C31⋊C9) | 3 |
| #21419226 | 3 |
| C35×C31 | 3 |
| C3×#6866 | 31 |