Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
560 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 61 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. C31⋊H(5,𝔽3) | C3 | semidirect |
| 2. #21419406 | C3 | semidirect |
| 3. #21419405 | C3 | semidirect |
| 4. #21419397 | C3 | semidirect |
| 5. C3×#14578894 | C3 | semidirect |
| 6. #21419308 | C3 | semidirect |
| 7. C3×C31×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×#11719689 | C32 | semidirect |
| 13. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 20. C34×C31 | C32 | semidirect |
| 21. C3×3−1+2×C31 | C32 | semidirect |
| 33. C32×C31⋊C3 | H(3,𝔽3) | semidirect |
| 37. H(3,𝔽3)×C31 | H(3,𝔽3) | semidirect |
| 48. C32⋊(C31⋊C3) | H(3,𝔽3) | semidirect |
| 78. C3×AΣL(1,𝔽27) | C31⋊C3 | semidirect |
| 89. C34 | C3×C31⋊C3 | semidirect |
| 91. C3×3−1+2 | C3×C31⋊C3 | semidirect |
| 105. C31 | UT(4,𝔽3) | semidirect |
| 131. H(3,𝔽3) | C32⋊(C31⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31⋊H(5,𝔽3) | 3 |
| #21419406 | 3 |
| #21419405 | 3 |
| #21419397 | 3 |
| C3×#14578894 | 3 |
| #21419308 | 3 |
| C3×C31×AΣL(1,𝔽27) | 3 |
| UT(4,𝔽3) | 31 |