Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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. C3×#14578891 | C3 | semidirect |
| 2. C3×#14578890 | C3 | semidirect |
| 3. C3×C27×C31⋊C3 | C3 | semidirect |
| 5. C32⋊(C31⋊C27) | C3 | semidirect |
| 6. (C3×C31⋊C3)⋊C27 | C3 | semidirect |
| 7. (C3×C31⋊C3)⋊C27 | C3 | semidirect |
| 8. (C3×C31⋊C3)⋊C27 | C3 | semidirect |
| 9. C3×C31×C27⋊C3 | C3 | semidirect |
| 47. C27×C31 | H(3,𝔽3) | semidirect |
| 64. C3×C31⋊C3 | C27⋊C3 | semidirect |
| 73. C3×C27⋊C3 | C31⋊C3 | semidirect |
| 105. C31 | C27⋊H(3,𝔽3) | semidirect |
| 128. C27 | C32⋊(C31⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#14578891 | 3 |
| C3×#14578890 | 3 |
| C3×C27×C31⋊C3 | 3 |
| C9×C32⋊(C31⋊C3) | 3 |
| C32⋊(C31⋊C27) | 3 |
| (C3×C31⋊C3)⋊C27 | 3 |
| C3×C31×C27⋊C3 | 3 |
| C27⋊H(3,𝔽3) | 31 |