Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1328 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 346 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. C32×#11719689 | C3 | semidirect |
| 2. C33×C31⋊C9 | C3 | semidirect |
| 3. #21419314 | C3 | direct (N × H) |
| 4. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 5. C3×C32⋊(C31⋊C9) | C3 | semidirect |
| 8. C3×#11719689 | C32 | semidirect |
| 13. C32×C31⋊C9 | C32 | semidirect |
| 14. C32⋊(C31⋊C9) | C32 | semidirect |
| 15. C32⋊(C31⋊C9) | C32 | semidirect |
| 25. C33×C31 | 3−1+2 | semidirect |
| 34. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 48. C32×C31 | C3×3−1+2 | semidirect |
| 53. C31⋊C9 | C3×H(3,𝔽3) | semidirect |
| 62. C3×C31 | C9⋊H(3,𝔽3) | semidirect |
| 79. C31 | C3×C9⋊H(3,𝔽3) | semidirect |
| 85. C33 | #11719689 | semidirect |
| 107. C32 | C3×#11719689 | semidirect |
| 115. C3 | #21419314 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11719689 | 3 |
| C33×C31⋊C9 | 3 |
| #21419314 | 3 |
| C3×C32⋊(C31⋊C9) | 3 |
| C32×H(3,𝔽3)×C31 | 3 |
| C3×C9⋊H(3,𝔽3) | 31 |