Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
456 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 70 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. #21419400 | C3 | semidirect |
| 2. #21419396 | C3 | semidirect |
| 3. #21419395 | C3 | semidirect |
| 4. C3×#14578899 | C3 | semidirect |
| 5. C3×#14578896 | C3 | semidirect |
| 6. #21419320 | C3 | semidirect |
| 7. C31×H(5,𝔽3) | C3 | semidirect |
| 8. C3×#11719689 | C32 | semidirect |
| 9. C3×#11719689 | C32 | semidirect |
| 10. C3×C32⋊(C31⋊C3) | C32 | semidirect |
| 11. C32×C31⋊C9 | C32 | semidirect |
| 67. H(5,𝔽3) | C31⋊C3 | semidirect |
| 98. C31 | #10624748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419400 | 3 |
| #21419396 | 3 |
| #21419395 | 3 |
| C3×#14578899 | 3 |
| C3×#14578896 | 3 |
| #21419320 | 3 |
| C31×H(5,𝔽3) | 3 |
| #10624748 | 31 |