Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
304 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 97 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. 3−1+2×C31⋊C9 | C3 | semidirect |
| 2. H(3,𝔽3)×C31⋊C9 | C3 | semidirect |
| 3. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 4. 3−1+2⋊(C31⋊C9) | C3 | semidirect |
| 5. H(3,𝔽3)⋊(C31⋊C9) | C3 | semidirect |
| 6. #21419226 | C3 | semidirect |
| 22. C31×AΣL(1,𝔽27) | C9 | semidirect |
| 28. C33×C31 | C3×C9 | semidirect |
| 31. 3−1+2×C31 | C3×C9 | semidirect |
| 83. AΣL(1,𝔽27) | C31⋊C9 | semidirect |
| 92. C31 | AΣL(1,𝔽27)⋊C9 | semidirect |
| 98. C33 | C3×C31⋊C9 | semidirect |
| 101. 3−1+2 | C3×C31⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×C31⋊C9 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| 3−1+2⋊(C31⋊C9) | 3 |
| H(3,𝔽3)⋊(C31⋊C9) | 3 |
| #21419226 | 3 |
| C3×C31×AΣL(1,𝔽27) | 3 |
| AΣL(1,𝔽27)⋊C9 | 31 |