Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 545 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. #26042115 | C2 | semidirect |
| 2. #26042096 | C2 | semidirect |
| 3. #26042091 | C2 | semidirect |
| 4. #26042084 | C2 | semidirect |
| 5. #26042079 | C2 | semidirect |
| 6. C2×#19153838 | C2 | semidirect |
| 7. C2×#131×C181 | C2 | semidirect |
| 9. #19153863 | C22 | semidirect |
| 10. #19153862 | C22 | semidirect |
| 12. C2×#15668449 | C22 | semidirect |
| 14. #19153849 | C22 | semidirect |
| 15. #19153844 | C22 | semidirect |
| 16. #19153838 | C22 | semidirect |
| 17. #19153838 | C22 | semidirect |
| 18. #19153838 | C22 | semidirect |
| 19. #19153838 | C22 | semidirect |
| 20. C2×Dic724 | C22 | semidirect |
| 21. C2×#15668438 | C22 | semidirect |
| 22. C2×D1448 | C22 | semidirect |
| 24. #131×C181 | C22 | semidirect |
| 25. #131×C181 | C22 | semidirect |
| 26. C2×M16×C181 | C22 | semidirect |
| 27. C22×C8×C181 | C22 | semidirect |
| 89. C181 | #3584 | semidirect |
| 97. C2×#131 | D181 | semidirect |
| 114. #131 | C2×D181 | semidirect |
| 115. #131 | C2×D181 | semidirect |
| 116. C2×M16 | C2×D181 | semidirect |
| 117. C22×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042115 | 2 |
| #26042096 | 2 |
| #26042091 | 2 |
| #26042084 | 2 |
| #26042079 | 2 |
| C2×#19153838 | 2 |
| C2×#131×C181 | 2 |
| #3584 | 181 |