Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
470 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 67 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×#14578913 | C3 | semidirect |
| 2. C3×#14578901 | C3 | semidirect |
| 3. C3×#14578901 | C3 | semidirect |
| 4. C3×#14578899 | C3 | semidirect |
| 5. C3×#14578898 | C3 | semidirect |
| 6. C3×#14578898 | C3 | semidirect |
| 7. C3×#14578896 | C3 | semidirect |
| 8. C3×#14578894 | C3 | semidirect |
| 9. C3×#14578894 | C3 | semidirect |
| 10. #21419323 | C3 | semidirect |
| 11. #21419320 | C3 | semidirect |
| 12. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 13. C3×C31×AΣL(1,𝔽27) | C3 | semidirect |
| 159. C3×AΣL(1,𝔽27) | C31⋊C3 | semidirect |
| 211. C31 | #10624746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578913 | 3 |
| C3×#14578901 | 3 |
| C3×#14578899 | 3 |
| C3×#14578898 | 3 |
| C3×#14578896 | 3 |
| C3×#14578894 | 3 |
| #21419323 | 3 |
| #21419320 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C3×C31×AΣL(1,𝔽27) | 3 |
| #10624746 | 31 |