Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041810 | C2 | semidirect |
| 2. C2×#19153803 | C2 | semidirect |
| 3. #26041662 | C2 | semidirect |
| 4. #26041632 | C2 | semidirect |
| 5. #26041500 | C2 | semidirect |
| 6. #26041492 | C2 | semidirect |
| 7. #26041437 | C2 | semidirect |
| 8. #26041430 | C2 | semidirect |
| 9. #26041417 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 13. C2×Dic724 | C22 | semidirect |
| 15. C2×#15668437 | C22 | semidirect |
| 17. #19153807 | C22 | semidirect |
| 22. #19153803 | C22 | semidirect |
| 25. #19153781 | C22 | semidirect |
| 27. D4×Dic181 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 143. C181 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041810 | 2 |
| C2×#19153803 | 2 |
| #26041662 | 2 |
| #26041632 | 2 |
| #26041500 | 2 |
| #26041492 | 2 |
| #26041437 | 2 |
| #26041430 | 2 |
| #26041417 | 2 |
| #26041329 | 2 |
| #447×C181 | 2 |
| #3211 | 181 |