Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 3. #26041676 | C2 | semidirect |
| 4. #26041628 | C2 | semidirect |
| 7. #26041565 | C2 | semidirect |
| 8. #26041564 | C2 | semidirect |
| 9. #26041561 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 128. C181 | #3229 | semidirect |
| 139. #475 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041833 | 2 |
| C4⋊Q8×D181 | 2 |
| #26041676 | 2 |
| #26041628 | 2 |
| #26041611 | 2 |
| #26041608 | 2 |
| #26041565 | 2 |
| #26041564 | 2 |
| #26041561 | 2 |
| #26041331 | 2 |
| #475×C181 | 2 |
| #3229 | 181 |