Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1166 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 292 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. C33×C31⋊C9 | C3 | semidirect |
| 3. #21419323 | C3 | semidirect |
| 4. #21419319 | C3 | semidirect |
| 5. #21419318 | C3 | semidirect |
| 6. #21419312 | C3 | semidirect |
| 8. #21419297 | C3 | semidirect |
| 9. C31×#6891 | C3 | semidirect |
| 12. C3×#11719686 | C32 | semidirect |
| 13. C3×#11719687 | C32 | semidirect |
| 22. C3×C9×C31⋊C3 | C32 | semidirect |
| 24. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 42. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 57. C32×C31 | #737 | semidirect |
| 73. #6891 | C31⋊C3 | semidirect |
| 99. C31 | #10624869 | semidirect |
| 130. C32 | #14578913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578913 | 3 |
| C33×C31⋊C9 | 3 |
| #21419323 | 3 |
| #21419319 | 3 |
| #21419318 | 3 |
| #21419312 | 3 |
| #21419308 | 3 |
| #21419297 | 3 |
| C31×#6891 | 3 |
| #10624869 | 31 |