Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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. #26042244 | C2 | semidirect |
| 4. C2×#19153870 | C2 | semidirect |
| 5. #26042155 | C2 | semidirect |
| 6. #26042149 | C2 | semidirect |
| 9. #19153903 | C4 | semidirect |
| 16. #19153880 | C4 | semidirect |
| 23. #19153741 | C4 | semidirect |
| 24. #19153739 | C4 | semidirect |
| 25. #19153737 | C4 | semidirect |
| 26. #102×C181 | C4 | semidirect |
| 109. C181 | #1765 | semidirect |
| 133. #102 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153903 | 2 |
| C2×#19153880 | 2 |
| #26042244 | 2 |
| C2×#19153870 | 2 |
| #26042155 | 2 |
| #26042149 | 2 |
| #26041272 | 2 |
| #1765 | 181 |