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. C32×#11719689 | C3 | semidirect |
| 2. C32×C32⋊(C31⋊C3) | C3 | semidirect |
| 3. C3×#14578894 | C3 | direct (N × H) |
| 4. C35×C31 | C3 | semidirect |
| 7. C3×#11719689 | C32 | semidirect |
| 9. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 11. #14578894 | C32 | direct (N × H) |
| 16. C34×C31 | C32 | semidirect |
| 26. C33×C31 | C33 | semidirect |
| 30. C32⋊(C31⋊C3) | C33 | semidirect |
| 32. #11719689 | C33 | semidirect |
| 41. C32×C31 | AΣL(1,𝔽27) | semidirect |
| 48. C35 | C31⋊C3 | semidirect |
| 55. C3×C31 | C3×AΣL(1,𝔽27) | semidirect |
| 63. C34 | C3×C31⋊C3 | semidirect |
| 70. C31 | C32×AΣL(1,𝔽27) | semidirect |
| 82. C33 | C32×C31⋊C3 | semidirect |
| 96. C32 | #14578894 | direct (N × H) |
| 105. C3 | C3×#14578894 | 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 |
| C3×#14578894 | 3 |
| C35×C31 | 3 |
| C32×AΣL(1,𝔽27) | 31 |