Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
322 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26041689 | C2 | semidirect |
| 4. #26041688 | C2 | semidirect |
| 5. #26041647 | C2 | semidirect |
| 8. #26041572 | C2 | semidirect |
| 9. #26041562 | C2 | semidirect |
| 11. #491×C181 | C2 | semidirect |
| 120. C181 | #3237 | semidirect |
| 127. #491 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041835 | 2 |
| #26041834 | 2 |
| #26041689 | 2 |
| #26041688 | 2 |
| #26041647 | 2 |
| #26041619 | 2 |
| #26041618 | 2 |
| #26041572 | 2 |
| #26041562 | 2 |
| #26041334 | 2 |
| #491×C181 | 2 |
| #3237 | 181 |