Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
2672 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 328 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. C34×C31⋊C3 | C3 | semidirect |
| 2. C32×#11719689 | C3 | semidirect |
| 3. C3×#14578893 | C3 | direct (N × H) |
| 4. C32×H(3,𝔽3)×C31 | C3 | semidirect |
| 8. C33×C31⋊C3 | C32 | semidirect |
| 10. C3×#11719689 | C32 | semidirect |
| 12. #14578893 | C32 | direct (N × H) |
| 16. C3×H(3,𝔽3)×C31 | C32 | semidirect |
| 28. C32×C31⋊C3 | C33 | semidirect |
| 30. H(3,𝔽3)×C31 | C33 | semidirect |
| 32. #11719689 | C33 | semidirect |
| 39. C32×C31 | AΣL(1,𝔽27) | semidirect |
| 50. C32×H(3,𝔽3) | C31⋊C3 | semidirect |
| 55. C3×C31 | C3×AΣL(1,𝔽27) | semidirect |
| 67. C3×H(3,𝔽3) | C3×C31⋊C3 | semidirect |
| 70. C31 | C32×AΣL(1,𝔽27) | semidirect |
| 86. H(3,𝔽3) | C32×C31⋊C3 | semidirect |
| 96. C32 | #14578893 | direct (N × H) |
| 105. C3 | C3×#14578893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C31⋊C3 | 3 |
| C32×#11719689 | 3 |
| C3×#14578893 | 3 |
| C32×H(3,𝔽3)×C31 | 3 |
| C32×AΣL(1,𝔽27) | 31 |