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. C22×#15668434 | C2 | semidirect |
| 3. #26041846 | C2 | semidirect |
| 4. #26041423 | C2 | semidirect |
| 5. #26041411 | C2 | semidirect |
| 6. #26041285 | C2 | semidirect |
| 7. #26041275 | C2 | semidirect |
| 8. #26041247 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C181 | C2 | semidirect |
| 12. C2×#15668450 | C22 | semidirect |
| 18. C2×D4×D181 | C22 | semidirect |
| 20. C2×#15668434 | C22 | semidirect |
| 21. C22×#13089678 | C22 | semidirect |
| 24. #19153787 | C22 | semidirect |
| 26. #19153775 | C22 | semidirect |
| 27. #19153740 | C22 | semidirect |
| 28. #19153738 | C22 | semidirect |
| 29. #19153737 | C22 | semidirect |
| 30. #19153728 | C22 | semidirect |
| 32. C22×D4×C181 | C22 | semidirect |
| 34. C2×SD16×C181 | C22 | semidirect |
| 35. C2×D8×C181 | C22 | semidirect |
| 36. C2×M16×C181 | C22 | semidirect |
| 50. C2×D724 | D4 | semidirect |
| 69. #41×C181 | D4 | semidirect |
| 151. C181 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D181 | semidirect |
| 172. C22×D4 | C2×D181 | semidirect |
| 174. C2×SD16 | C2×D181 | semidirect |
| 177. C2×D8 | C2×D181 | semidirect |
| 178. C2×M16 | C2×D181 | semidirect |
| 198. #41 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153862 | 2 |
| C22×#15668434 | 2 |
| #26041846 | 2 |
| #26041423 | 2 |
| #26041411 | 2 |
| #26041285 | 2 |
| #26041275 | 2 |
| #26041247 | 2 |
| C2×AGL(1,ℤ/8)×C181 | 2 |
| #3008 | 181 |