Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. #26042096 | C2 | semidirect |
| 2. #26041719 | C2 | semidirect |
| 3. #26041715 | C2 | semidirect |
| 4. #26041709 | C2 | semidirect |
| 5. C2×#19153760 | C2 | semidirect |
| 6. #26041696 | C2 | semidirect |
| 7. #576×C181 | C2 | semidirect |
| 10. #19153838 | C22 | semidirect |
| 11. C2×Dic724 | C22 | semidirect |
| 12. #19153762 | C22 | semidirect |
| 13. #19153760 | C22 | semidirect |
| 14. #19153760 | C22 | semidirect |
| 15. #19153759 | C22 | semidirect |
| 16. #19153757 | C22 | semidirect |
| 17. #19153756 | C22 | semidirect |
| 18. C2×#15668424 | C22 | semidirect |
| 74. C181 | #3416 | semidirect |
| 77. #576 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042096 | 2 |
| #26041719 | 2 |
| #26041715 | 2 |
| #26041709 | 2 |
| C2×#19153760 | 2 |
| #26041696 | 2 |
| #576×C181 | 2 |
| #3416 | 181 |