Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19153838 | C2 | semidirect |
| 2. C2×#19153835 | C2 | semidirect |
| 3. #26041947 | C2 | semidirect |
| 4. #26041654 | C2 | semidirect |
| 5. #26041516 | C2 | semidirect |
| 6. #26041478 | C2 | semidirect |
| 7. #26041425 | C2 | semidirect |
| 8. #26041422 | C2 | semidirect |
| 9. #26041373 | C2 | semidirect |
| 10. C8×C22⋊D181 | C2 | semidirect |
| 11. #466×C181 | C2 | semidirect |
| 56. Dic724 | D4 | semidirect |
| 134. Dic181 | #135 | semidirect |
| 142. C181 | #3287 | semidirect |
| 149. #466 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| C2×#19153835 | 2 |
| #26041947 | 2 |
| #26041654 | 2 |
| #26041516 | 2 |
| #26041478 | 2 |
| #26041425 | 2 |
| #26041422 | 2 |
| #26041373 | 2 |
| C8×C22⋊D181 | 2 |
| #466×C181 | 2 |
| #3287 | 181 |