Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153849 | C2 | semidirect |
| 3. C2×#19153804 | C2 | semidirect |
| 4. C4×#15668449 | C2 | semidirect |
| 5. #26041502 | C2 | semidirect |
| 6. #26041495 | C2 | semidirect |
| 7. #26041289 | C2 | semidirect |
| 8. #26041285 | C2 | semidirect |
| 9. #423×C181 | C2 | semidirect |
| 15. C2×Dic724 | C22 | semidirect |
| 17. C2×#15668438 | C22 | semidirect |
| 22. C4×Dic362 | C22 | semidirect |
| 23. C4×D724 | C22 | semidirect |
| 29. #19153741 | C22 | semidirect |
| 34. C4⋊C8×C181 | C22 | semidirect |
| 125. C181 | #3040 | semidirect |
| 133. #423 | D181 | semidirect |
| 158. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153844 | 2 |
| C2×#19153804 | 2 |
| C4×#15668449 | 2 |
| #26041502 | 2 |
| #26041495 | 2 |
| #26041289 | 2 |
| #26041285 | 2 |
| #423×C181 | 2 |
| #3040 | 181 |