Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
1196 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1196 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. C32×#11719689 | C3 | semidirect |
| 2. C32×C32⋊(C31⋊C3) | C3 | semidirect |
| 3. #21419395 | C3 | direct (N × H) |
| 4. C3×#14578893 | C3 | semidirect |
| 5. C32×H(3,𝔽3)×C31 | C3 | semidirect |
| 6. C33×C31⋊C3 | C32 | semidirect |
| 10. C3×#11719689 | C32 | semidirect |
| 11. C3×#11719689 | C32 | semidirect |
| 15. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 17. #14578893 | C32 | semidirect |
| 23. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 36. C32×C31⋊C3 | C33 | semidirect |
| 45. #11719689 | C33 | semidirect |
| 69. C32×H(3,𝔽3) | C31⋊C3 | semidirect |
| 77. C3×C31 | #6909 | semidirect |
| 95. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 98. C31 | C3×#6909 | semidirect |
| 147. C3 | #21419395 | 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 |
| C32×C32⋊(C31⋊C3) | 3 |
| #21419395 | 3 |
| C3×#14578893 | 3 |
| C32×H(3,𝔽3)×C31 | 3 |
| C3×#6909 | 31 |