Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1166 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 310 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. #21419322 | C3 | semidirect |
| 3. #21419317 | C3 | semidirect |
| 4. #21419316 | C3 | semidirect |
| 5. #21419312 | C3 | semidirect |
| 7. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 8. C33×C9×C31 | C3 | semidirect |
| 11. C3×#11719686 | C32 | semidirect |
| 12. C3×#11719687 | C32 | semidirect |
| 15. C3×C9×C31⋊C3 | C32 | semidirect |
| 17. (C3×C31⋊C3)⋊C9 | C32 | semidirect |
| 34. C3×C9×C31 | H(3,𝔽3) | semidirect |
| 52. C32×C31 | #737 | semidirect |
| 62. C33×C9 | C31⋊C3 | semidirect |
| 90. C31 | #10624869 | semidirect |
| 107. C3×C9 | C32⋊(C31⋊C3) | semidirect |
| 119. C32 | #14578912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578912 | 3 |
| #21419322 | 3 |
| #21419317 | 3 |
| #21419316 | 3 |
| #21419312 | 3 |
| #21419308 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| C33×C9×C31 | 3 |
| #10624869 | 31 |