Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153842 | C2 | semidirect |
| 2. C2×#19153838 | C2 | semidirect |
| 3. #26041846 | C2 | semidirect |
| 4. #26041760 | C2 | semidirect |
| 5. #26041500 | C2 | semidirect |
| 6. #26041493 | C2 | semidirect |
| 7. #26041478 | C2 | semidirect |
| 8. #26041473 | C2 | semidirect |
| 9. #26041305 | C2 | semidirect |
| 10. #26041278 | C2 | semidirect |
| 11. C2×#102×C181 | C2 | semidirect |
| 16. C2×Dic724 | C22 | semidirect |
| 17. C2×#15668438 | C22 | semidirect |
| 18. C2×#15668438 | C22 | semidirect |
| 20. C2×D1448 | C22 | semidirect |
| 28. #19153781 | C22 | semidirect |
| 29. #19153778 | C22 | semidirect |
| 34. #19153745 | C22 | semidirect |
| 35. #19153745 | C22 | semidirect |
| 36. #19153739 | C22 | semidirect |
| 37. #19153736 | C22 | semidirect |
| 46. #15668449 | D4 | semidirect |
| 154. C181 | #3045 | semidirect |
| 166. C2×#102 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| C2×#19153838 | 2 |
| #26041846 | 2 |
| #26041760 | 2 |
| #26041500 | 2 |
| #26041493 | 2 |
| #26041478 | 2 |
| #26041473 | 2 |
| #26041305 | 2 |
| #26041278 | 2 |
| C2×#102×C181 | 2 |
| #3045 | 181 |