Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
668 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 668 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. C32×C32⋊(C31⋊C3) | C3 | semidirect |
| 2. #21419312 | C3 | semidirect |
| 3. #21419200 | C3 | semidirect |
| 4. C32×H(3,𝔽3)×C31 | C3 | semidirect |
| 10. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 13. C32⋊(C31⋊C9) | C32 | semidirect |
| 19. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 68. C32×H(3,𝔽3) | C31⋊C3 | semidirect |
| 91. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 95. C31 | #10624589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C31⋊C3) | 3 |
| #21419312 | 3 |
| #21419200 | 3 |
| C32×H(3,𝔽3)×C31 | 3 |
| #10624589 | 31 |