Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
472 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. C9×#11719689 | C3 | semidirect |
| 3. C9×C32⋊(C31⋊C3) | C3 | semidirect |
| 4. #21419238 | C3 | semidirect |
| 5. #21419235 | C3 | semidirect |
| 6. #21419226 | C3 | semidirect |
| 7. C33×C9×C31 | C3 | semidirect |
| 11. #14578894 | C9 | direct (N × H) |
| 27. C33×C31 | C3×C9 | semidirect |
| 38. C32⋊(C31⋊C3) | C3×C9 | semidirect |
| 40. #11719689 | C3×C9 | semidirect |
| 61. C9×C31 | AΣL(1,𝔽27) | semidirect |
| 65. C33×C9 | C31⋊C3 | semidirect |
| 94. C31 | C9×AΣL(1,𝔽27) | semidirect |
| 100. C33 | C9×C31⋊C3 | semidirect |
| 135. C9 | #14578894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578894 | 3 |
| C9×#11719689 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| #21419238 | 3 |
| #21419235 | 3 |
| #21419226 | 3 |
| C33×C9×C31 | 3 |
| C9×AΣL(1,𝔽27) | 31 |