Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26041563 | C2 | semidirect |
| 4. #26041561 | C2 | semidirect |
| 7. #26041490 | C2 | semidirect |
| 8. #26041489 | C2 | semidirect |
| 9. #26041488 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 129. C181 | #3255 | semidirect |
| 135. #475 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #26041833 | 2 |
| #26041563 | 2 |
| #26041561 | 2 |
| #26041538 | 2 |
| #26041536 | 2 |
| #26041490 | 2 |
| #26041489 | 2 |
| #26041488 | 2 |
| #26041301 | 2 |
| #475×C181 | 2 |
| #3255 | 181 |