Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
212 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 49 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. #733×C31⋊C3 | C3 | semidirect |
| 3. C9⋊C9×C31⋊C3 | C3 | semidirect |
| 4. #21419283 | C3 | semidirect |
| 5. #21419282 | C3 | semidirect |
| 6. #21419281 | C3 | semidirect |
| 7. #21419280 | C3 | semidirect |
| 8. #21419279 | C3 | semidirect |
| 9. C31×#6883 | C3 | semidirect |
| 14. #14578902 | C32 | semidirect |
| 15. #14578902 | C32 | semidirect |
| 19. #14578887 | C32 | semidirect |
| 20. #14578886 | C32 | semidirect |
| 22. C31×#733 | C32 | semidirect |
| 24. C31×C9⋊C9 | C32 | semidirect |
| 71. #6883 | C31⋊C3 | direct (N × H) |
| 78. C31⋊C3 | #6883 | direct (N × H) |
| 86. #733 | C3×C31⋊C3 | semidirect |
| 93. C9⋊C9 | C3×C31⋊C3 | semidirect |
| 94. C31 | C3×#6883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #733×C31⋊C3 | 3 |
| #732×C31⋊C3 | 3 |
| C9⋊C9×C31⋊C3 | 3 |
| #21419283 | 3 |
| #21419282 | 3 |
| #21419281 | 3 |
| #21419280 | 3 |
| #21419279 | 3 |
| C31×#6883 | 3 |
| C3×#6883 | 31 |