Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
758 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 758 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 |
|---|---|---|
| 1. C32×#11719689 | C3 | semidirect |
| 3. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 4. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 5. C3×C31×C32⋊C9 | C3 | semidirect |
| 29. C32×C31⋊C3 | 3−1+2 | semidirect |
| 38. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 63. C3×C32⋊C9 | C31⋊C3 | semidirect |
| 83. C31 | #10624563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| C32×C32⋊(C31⋊C3) | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C3×C31×C32⋊C9 | 3 |
| #10624563 | 31 |