Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1196 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 274 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. C3×3−1+2×C31⋊C3 | C3 | semidirect |
| 2. C32×C32⋊(C31⋊C3) | C3 | semidirect |
| 3. C3×H(3,𝔽3)×C31⋊C3 | C3 | semidirect |
| 4. #21419394 | C3 | direct (N × H) |
| 5. C3×#14578895 | C3 | semidirect |
| 6. C3×#14578894 | C3 | semidirect |
| 7. C3×#14578893 | C3 | semidirect |
| 8. C3×C31×AΣL(1,𝔽27) | C3 | semidirect |
| 11. C33×C31⋊C3 | C32 | semidirect |
| 12. C3×#11719689 | C32 | semidirect |
| 16. 3−1+2×C31⋊C3 | C32 | semidirect |
| 22. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 24. H(3,𝔽3)×C31⋊C3 | C32 | semidirect |
| 26. #14578895 | C32 | semidirect |
| 27. #14578894 | C32 | semidirect |
| 28. #14578893 | C32 | semidirect |
| 29. C34×C31 | C32 | semidirect |
| 30. C3×3−1+2×C31 | C32 | semidirect |
| 32. C31×AΣL(1,𝔽27) | C32 | semidirect |
| 38. C33×C31 | C33 | semidirect |
| 50. C32×C31⋊C3 | C33 | semidirect |
| 52. 3−1+2×C31 | C33 | semidirect |
| 62. #11719689 | C33 | semidirect |
| 100. C3×AΣL(1,𝔽27) | C31⋊C3 | semidirect |
| 105. C3×C31 | #6909 | semidirect |
| 114. C34 | C3×C31⋊C3 | semidirect |
| 120. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 134. AΣL(1,𝔽27) | C3×C31⋊C3 | semidirect |
| 135. C31 | C3×#6909 | semidirect |
| 153. C33 | C32×C31⋊C3 | semidirect |
| 159. 3−1+2 | C32×C31⋊C3 | semidirect |
| 203. C3 | #21419394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C31⋊C3 | 3 |
| C32×C32⋊(C31⋊C3) | 3 |
| C3×H(3,𝔽3)×C31⋊C3 | 3 |
| #21419394 | 3 |
| C3×#14578895 | 3 |
| C3×#14578894 | 3 |
| C3×#14578893 | 3 |
| C3×C31×AΣL(1,𝔽27) | 3 |
| C3×#6909 | 31 |