Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
506 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 64 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. #21419312 | C3 | semidirect |
| 2. #21419308 | C3 | semidirect |
| 3. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 4. #21419200 | C3 | semidirect |
| 5. C32×H(3,𝔽3)×C31 | C3 | semidirect |
| 10. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 16. C32⋊(C31⋊C9) | C32 | semidirect |
| 17. C32⋊(C31⋊C9) | C32 | semidirect |
| 79. C32×H(3,𝔽3) | C31⋊C3 | semidirect |
| 112. C31 | #10624596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419312 | 3 |
| #21419308 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| #21419200 | 3 |
| C32×H(3,𝔽3)×C31 | 3 |
| #10624596 | 31 |