Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#19153824 | C2 | semidirect |
| 3. #26041858 | C2 | semidirect |
| 4. #26041538 | C2 | semidirect |
| 5. #26041537 | C2 | semidirect |
| 6. #26041529 | C2 | semidirect |
| 7. #26041507 | C2 | semidirect |
| 8. #26041506 | C2 | semidirect |
| 9. #106×D181 | C2 | semidirect |
| 10. #26041277 | C2 | semidirect |
| 11. #469×C181 | C2 | semidirect |
| 64. C8×D181 | D4 | semidirect |
| 139. C181 | #3060 | semidirect |
| 147. #469 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153835 | 2 |
| C2×#19153824 | 2 |
| #26041858 | 2 |
| #26041538 | 2 |
| #26041537 | 2 |
| #26041529 | 2 |
| #26041507 | 2 |
| #26041506 | 2 |
| #106×D181 | 2 |
| #26041277 | 2 |
| #469×C181 | 2 |
| #3060 | 181 |