Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1328 conjugacy classes of subgroups; only the 364 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 364 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. #21419317 | C3 | direct (N × H) |
| 4. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 5. C3×(C3×C31⋊C3)⋊C9 | C3 | semidirect |
| 6. C33×C9×C31 | C3 | semidirect |
| 9. C3×#11719687 | C32 | semidirect |
| 13. C32⋊(C31⋊C9) | C32 | semidirect |
| 14. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 19. C32×C9×C31 | C32 | semidirect |
| 22. C33×C31 | 3−1+2 | semidirect |
| 31. C3×C9×C31 | H(3,𝔽3) | semidirect |
| 44. C32×C31 | C3×3−1+2 | semidirect |
| 52. C9×C31 | C3×H(3,𝔽3) | semidirect |
| 56. C33×C9 | C31⋊C3 | semidirect |
| 61. C3×C31 | C9⋊H(3,𝔽3) | semidirect |
| 76. C32×C9 | C3×C31⋊C3 | semidirect |
| 79. C31 | C3×C9⋊H(3,𝔽3) | semidirect |
| 86. C33 | #11719687 | semidirect |
| 95. C3×C9 | C32⋊(C31⋊C3) | semidirect |
| 107. C32 | C3×#11719687 | semidirect |
| 112. C9 | C3×C32⋊(C31⋊C3) | semidirect |
| 115. C3 | #21419317 | 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 |
| #21419317 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×(C3×C31⋊C3)⋊C9 | 3 |
| C33×C9×C31 | 3 |
| C3×C9⋊H(3,𝔽3) | 31 |