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. #21419395 | C3 | semidirect |
| 5. #21419395 | C3 | semidirect |
| 6. C3×#14578899 | C3 | semidirect |
| 7. C3×#14578896 | C3 | semidirect |
| 8. #21419323 | C3 | semidirect |
| 9. C31×#6909 | C3 | semidirect |
| 10. C3×#11719689 | C32 | semidirect |
| 11. C3×#11719689 | C32 | semidirect |
| 15. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 18. C32×C31⋊C9 | C32 | semidirect |
| 26. C3×3−1+2×C31 | C32 | semidirect |
| 28. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 89. #6909 | C31⋊C3 | semidirect |
| 104. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 112. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 122. 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 |
| #21419395 | 3 |
| C3×#14578899 | 3 |
| C3×#14578896 | 3 |
| #21419323 | 3 |
| C31×#6909 | 3 |
| #10624748 | 31 |