Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#19153844 | C2 | semidirect |
| 2. #26041857 | C2 | semidirect |
| 3. #26041843 | C2 | semidirect |
| 4. #26041532 | C2 | semidirect |
| 5. #26041525 | C2 | semidirect |
| 6. #26041515 | C2 | semidirect |
| 7. #26041508 | C2 | semidirect |
| 8. #26041321 | C2 | semidirect |
| 9. #26041276 | C2 | semidirect |
| 10. C2×#19153738 | C2 | semidirect |
| 11. C2×#131×C181 | C2 | semidirect |
| 19. #19153795 | C22 | semidirect |
| 23. #19153790 | C22 | semidirect |
| 29. #19153750 | C22 | semidirect |
| 30. #19153748 | C22 | semidirect |
| 31. #19153741 | C22 | semidirect |
| 32. #19153741 | C22 | semidirect |
| 35. #19153738 | C22 | semidirect |
| 36. #19153738 | C22 | semidirect |
| 40. C2×M16×C181 | C22 | semidirect |
| 42. C22×C8×C181 | C22 | semidirect |
| 79. M16×C181 | D4 | semidirect |
| 151. C181 | #3062 | semidirect |
| 154. C2×#131 | D181 | semidirect |
| 172. C2×M16 | C2×D181 | semidirect |
| 174. C22×C8 | C2×D181 | semidirect |
| 220. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| #26041857 | 2 |
| #26041843 | 2 |
| #26041532 | 2 |
| #26041525 | 2 |
| #26041515 | 2 |
| #26041508 | 2 |
| #26041321 | 2 |
| #26041276 | 2 |
| C2×#19153738 | 2 |
| C2×#131×C181 | 2 |
| #3062 | 181 |