Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #26041235 | C2 | semidirect |
| 5. C2×#19153727 | C2 | semidirect |
| 6. #26041043 | C2 | semidirect |
| 7. #339×C181 | C2 | semidirect |
| 10. #19153824 | C4 | semidirect |
| 16. #19153744 | C4 | semidirect |
| 17. #19153739 | C4 | semidirect |
| 18. #19153736 | C4 | semidirect |
| 98. C181 | #1765 | semidirect |
| 106. #339 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153824 | 2 |
| C2×#19153744 | 2 |
| #26041273 | 2 |
| #26041235 | 2 |
| C2×#19153727 | 2 |
| #26041043 | 2 |
| #339×C181 | 2 |
| #1765 | 181 |