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×#14578911 | C3 | semidirect |
| 2. C33×C31⋊C9 | C3 | semidirect |
| 3. #21419320 | C3 | semidirect |
| 4. #21419314 | C3 | semidirect |
| 5. #21419312 | C3 | semidirect |
| 6. H(3,𝔽3)×C31⋊C9 | C3 | semidirect |
| 10. C3×#11719689 | C32 | semidirect |
| 16. C32×C31⋊C9 | C32 | semidirect |
| 18. C32⋊(C31⋊C9) | C32 | semidirect |
| 35. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 48. C32×C31 | #737 | semidirect |
| 80. C31 | #10624869 | semidirect |
| 106. C32 | #14578911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578911 | 3 |
| C33×C31⋊C9 | 3 |
| #21419320 | 3 |
| #21419314 | 3 |
| #21419312 | 3 |
| H(3,𝔽3)×C31⋊C9 | 3 |
| C31×C32⋊H(3,𝔽3) | 3 |
| #10624869 | 31 |