Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153862 | C2 | semidirect |
| 2. C2×#19153841 | C2 | semidirect |
| 3. C22×D1448 | C2 | semidirect |
| 4. #26041848 | C2 | semidirect |
| 5. #26041427 | C2 | semidirect |
| 6. #26041414 | C2 | semidirect |
| 7. #26041283 | C2 | semidirect |
| 8. #26041245 | C2 | semidirect |
| 9. #416×C181 | C2 | semidirect |
| 12. C2×#15668450 | C22 | semidirect |
| 17. C22×D724 | C22 | semidirect |
| 19. C2×D4×D181 | C22 | semidirect |
| 21. C2×#15668436 | C22 | semidirect |
| 23. C2×D1448 | C22 | semidirect |
| 24. C2×#15668434 | C22 | semidirect |
| 25. C2×#15668433 | C22 | semidirect |
| 28. #19153791 | C22 | semidirect |
| 30. #19153736 | C22 | semidirect |
| 31. #19153728 | C22 | semidirect |
| 33. C22×C8×C181 | C22 | semidirect |
| 34. #117×C181 | C22 | semidirect |
| 35. #103×C181 | C22 | semidirect |
| 36. #102×C181 | C22 | semidirect |
| 55. C2×D724 | D4 | semidirect |
| 72. #41×C181 | D4 | semidirect |
| 151. C181 | #3008 | semidirect |
| 160. #416 | D181 | semidirect |
| 179. C22×C8 | C2×D181 | semidirect |
| 184. #117 | C2×D181 | semidirect |
| 185. #103 | C2×D181 | semidirect |
| 187. #102 | C2×D181 | semidirect |
| 198. #41 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153862 | 2 |
| C2×#19153841 | 2 |
| C22×D1448 | 2 |
| #26041848 | 2 |
| #26041427 | 2 |
| #26041414 | 2 |
| #26041283 | 2 |
| #26041245 | 2 |
| #416×C181 | 2 |
| #3008 | 181 |