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×#19153861 | C2 | semidirect |
| 2. C2×#19153844 | C2 | semidirect |
| 3. C22×#15668434 | C2 | semidirect |
| 4. #26041848 | C2 | semidirect |
| 5. #26041425 | C2 | semidirect |
| 6. #26041414 | C2 | semidirect |
| 7. #26041273 | C2 | semidirect |
| 8. #26041247 | C2 | semidirect |
| 9. #418×C181 | C2 | semidirect |
| 15. C2×#15668448 | C22 | semidirect |
| 16. C22×D724 | C22 | semidirect |
| 19. C2×D4×D181 | C22 | semidirect |
| 21. C2×#15668438 | C22 | semidirect |
| 22. C2×D1448 | C22 | semidirect |
| 24. C2×#15668434 | C22 | semidirect |
| 25. C22×#13089678 | C22 | semidirect |
| 28. #19153791 | C22 | semidirect |
| 30. #19153739 | C22 | semidirect |
| 31. #19153736 | C22 | semidirect |
| 32. #19153728 | C22 | semidirect |
| 34. C2×M16×C181 | C22 | semidirect |
| 35. #117×C181 | C22 | semidirect |
| 36. #102×C181 | C22 | semidirect |
| 42. #15668449 | D4 | semidirect |
| 75. C2×D4×C181 | D4 | semidirect |
| 151. C181 | #3008 | semidirect |
| 159. #418 | D181 | semidirect |
| 178. C2×M16 | C2×D181 | semidirect |
| 184. #117 | C2×D181 | semidirect |
| 187. #102 | C2×D181 | semidirect |
| 218. C2×D4 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153861 | 2 |
| C2×#19153844 | 2 |
| C22×#15668434 | 2 |
| #26041848 | 2 |
| #26041425 | 2 |
| #26041414 | 2 |
| #26041273 | 2 |
| #26041247 | 2 |
| #418×C181 | 2 |
| #3008 | 181 |