Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041234 | C2 | semidirect |
| 4. C2×#19153726 | C2 | semidirect |
| 5. #26041043 | C2 | semidirect |
| 6. #26041040 | C2 | semidirect |
| 12. #19153743 | C4 | semidirect |
| 13. #19153740 | C4 | semidirect |
| 14. #19153737 | C4 | semidirect |
| 20. #131×C181 | C4 | semidirect |
| 98. C181 | #1765 | semidirect |
| 109. #131 | Dic181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153743 | 2 |
| #26041275 | 2 |
| #26041234 | 2 |
| C2×#19153726 | 2 |
| #26041043 | 2 |
| #26041040 | 2 |
| C2×#131×C181 | 2 |
| #1765 | 181 |