Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
506 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 55 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×H(3,𝔽3)×C31⋊C3 | C3 | semidirect |
| 2. #21419310 | C3 | semidirect |
| 3. (C3×C31⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 4. C32⋊C9×C31⋊C3 | C3 | semidirect |
| 5. #21419201 | C3 | semidirect |
| 6. #21419201 | C3 | semidirect |
| 7. #21419200 | C3 | semidirect |
| 8. #21419200 | C3 | semidirect |
| 9. C31×#6856 | C3 | semidirect |
| 19. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 22. C32⋊(C31⋊C9) | C32 | semidirect |
| 23. C32⋊(C31⋊C9) | C32 | semidirect |
| 29. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 30. C31×C32⋊C9 | C32 | semidirect |
| 31. C31×C32⋊C9 | C32 | semidirect |
| 111. #6856 | C31⋊C3 | semidirect |
| 136. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 144. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 145. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 146. C31 | #10624596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| #21419310 | 3 |
| (C3×C31⋊C3)⋊H(3,𝔽3) | 3 |
| C32⋊C9×C31⋊C3 | 3 |
| #21419201 | 3 |
| #21419200 | 3 |
| C31×#6856 | 3 |
| #10624596 | 31 |