Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #26041182 | C2 | semidirect |
| 3. #26041179 | C2 | semidirect |
| 4. #26041173 | C2 | semidirect |
| 5. #26041171 | C2 | semidirect |
| 6. #26041168 | C2 | semidirect |
| 7. #26041158 | C2 | semidirect |
| 8. #26041134 | C2 | semidirect |
| 9. #386×C181 | C2 | semidirect |
| 12. #19153784 | C4 | semidirect |
| 13. C2×C4⋊Dic181 | C22 | semidirect |
| 14. C2×#15668428 | C22 | semidirect |
| 17. C2×C22⋊Dic181 | C22 | semidirect |
| 23. C2×C4×Dic181 | C22 | semidirect |
| 24. C2×C4×Dic181 | C22 | semidirect |
| 25. #19153723 | C22 | semidirect |
| 26. #19153723 | C22 | semidirect |
| 28. C23×C4×C181 | C22 | semidirect |
| 30. C2×C22⋊C4×C181 | C22 | semidirect |
| 31. #95×C181 | C22 | semidirect |
| 36. C23×D181 | C2×C4 | semidirect |
| 48. C22⋊Dic181 | C2×C4 | semidirect |
| 53. #15668426 | C2×C4 | semidirect |
| 149. C181 | #2375 | semidirect |
| 158. #386 | D181 | semidirect |
| 163. C23×C4 | C2×D181 | semidirect |
| 176. C2×C22⋊C4 | C2×D181 | semidirect |
| 181. #95 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153784 | 2 |
| #26041182 | 2 |
| #26041179 | 2 |
| #26041173 | 2 |
| #26041171 | 2 |
| #26041168 | 2 |
| #26041158 | 2 |
| #26041134 | 2 |
| #386×C181 | 2 |
| #2375 | 181 |