Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19153835 | C2 | semidirect |
| 2. C22×Dic724 | C2 | semidirect |
| 3. #26041935 | C2 | semidirect |
| 4. #26041662 | C2 | semidirect |
| 5. #26041521 | C2 | semidirect |
| 6. #26041500 | C2 | semidirect |
| 7. #26041442 | C2 | semidirect |
| 8. #26041417 | C2 | semidirect |
| 9. #26041373 | C2 | semidirect |
| 10. C8×C22⋊D181 | C2 | semidirect |
| 11. #466×C181 | C2 | semidirect |
| 55. Dic724 | D4 | semidirect |
| 116. C22×C181 | #135 | semidirect |
| 136. C181 | #3285 | semidirect |
| 143. #466 | D181 | semidirect |
| 256. C22 | #19153835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153835 | 2 |
| C22×Dic724 | 2 |
| #26041935 | 2 |
| #26041662 | 2 |
| #26041521 | 2 |
| #26041500 | 2 |
| #26041442 | 2 |
| #26041417 | 2 |
| #26041373 | 2 |
| C8×C22⋊D181 | 2 |
| #466×C181 | 2 |
| #3285 | 181 |