Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1328 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 346 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×#11719687 | C3 | semidirect |
| 3. C33×C31⋊C9 | C3 | semidirect |
| 4. #21419318 | C3 | direct (N × H) |
| 5. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 6. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 7. C3×C31×C32⋊C9 | C3 | semidirect |
| 10. C3×#11719687 | C32 | semidirect |
| 17. C32×C31⋊C9 | C32 | semidirect |
| 18. C32⋊(C31⋊C9) | C32 | semidirect |
| 19. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 22. C31×C32⋊C9 | C32 | semidirect |
| 25. C33×C31 | 3−1+2 | semidirect |
| 38. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 49. C32×C31 | C3×3−1+2 | semidirect |
| 59. C31⋊C9 | C3×H(3,𝔽3) | semidirect |
| 66. C3×C32⋊C9 | C31⋊C3 | semidirect |
| 68. C3×C31 | C9⋊H(3,𝔽3) | semidirect |
| 87. C32⋊C9 | C3×C31⋊C3 | semidirect |
| 88. C31 | C3×C9⋊H(3,𝔽3) | semidirect |
| 95. C33 | #11719687 | semidirect |
| 118. C32 | C3×#11719687 | semidirect |
| 127. C3 | #21419318 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719687 | 3 |
| C32×C32⋊(C31⋊C3) | 3 |
| C33×C31⋊C9 | 3 |
| #21419318 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C3×C31×C32⋊C9 | 3 |
| C3×C9⋊H(3,𝔽3) | 31 |