Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
456 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 61 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. C31⋊H(5,𝔽3) | C3 | semidirect |
| 2. #21419402 | C3 | semidirect |
| 3. #21419397 | C3 | semidirect |
| 4. #21419397 | C3 | semidirect |
| 5. #21419396 | C3 | semidirect |
| 6. C3×#14578900 | C3 | semidirect |
| 7. C3×#14578897 | C3 | semidirect |
| 8. #21419322 | C3 | semidirect |
| 9. C31×#6893 | C3 | semidirect |
| 10. C3×#11719689 | C32 | semidirect |
| 11. C3×#11719689 | C32 | semidirect |
| 16. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 27. C3×3−1+2×C31 | C32 | semidirect |
| 29. C32×C9×C31 | C32 | semidirect |
| 99. #6893 | C31⋊C3 | semidirect |
| 112. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 122. C32×C9 | C3×C31⋊C3 | semidirect |
| 131. C31 | #10624748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31⋊H(5,𝔽3) | 3 |
| #21419402 | 3 |
| #21419397 | 3 |
| #21419396 | 3 |
| C3×#14578900 | 3 |
| C3×#14578897 | 3 |
| #21419322 | 3 |
| C31×#6893 | 3 |
| #10624748 | 31 |