Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
414 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 414 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. #21419437 | C3 | semidirect |
| 2. #21419409 | C3 | semidirect |
| 3. #21419409 | C3 | semidirect |
| 5. #21419402 | C3 | semidirect |
| 6. #21419402 | C3 | semidirect |
| 7. #21419402 | C3 | semidirect |
| 8. #21419400 | C3 | semidirect |
| 9. C3×#14578901 | C3 | semidirect |
| 10. C3×#14578898 | C3 | semidirect |
| 11. #21419323 | C3 | semidirect |
| 12. #21419320 | C3 | semidirect |
| 13. C31×#6910 | C3 | semidirect |
| 129. #6910 | C31⋊C3 | semidirect |
| 171. C31 | #10624751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419437 | 3 |
| #21419409 | 3 |
| #21419405 | 3 |
| #21419402 | 3 |
| #21419400 | 3 |
| C3×#14578901 | 3 |
| C3×#14578898 | 3 |
| #21419323 | 3 |
| #21419320 | 3 |
| C31×#6910 | 3 |
| #10624751 | 31 |