Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1166 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 301 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×#14578912 | C3 | semidirect |
| 2. C32×C9×C31⋊C3 | C3 | semidirect |
| 3. #21419323 | C3 | semidirect |
| 4. #21419320 | C3 | semidirect |
| 5. #21419313 | C3 | semidirect |
| 6. #21419309 | C3 | semidirect |
| 8. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 9. C3×C31×#737 | C3 | semidirect |
| 13. C3×#11719686 | C32 | semidirect |
| 14. C3×#11719687 | C32 | semidirect |
| 21. C3×C9×C31⋊C3 | C32 | semidirect |
| 22. C32⋊(C31⋊C9) | C32 | semidirect |
| 24. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 27. C3×3−1+2×C31 | C32 | semidirect |
| 30. C32×C9×C31 | C32 | semidirect |
| 41. C3×C9×C31 | H(3,𝔽3) | semidirect |
| 67. C3×C31⋊C3 | #737 | semidirect |
| 74. C3×#737 | C31⋊C3 | semidirect |
| 95. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 105. C32×C9 | C3×C31⋊C3 | semidirect |
| 109. C31 | #10624869 | semidirect |
| 131. C3×C9 | C32⋊(C31⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| C32×C9×C31⋊C3 | 3 |
| #21419323 | 3 |
| #21419320 | 3 |
| #21419313 | 3 |
| #21419309 | 3 |
| (C3×C31⋊C3)⋊H(3,𝔽3) | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| C3×C31×#737 | 3 |
| #10624869 | 31 |