Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041995 | C2 | semidirect |
| 2. D4×D724 | C2 | semidirect |
| 3. #26041627 | C2 | semidirect |
| 4. #26041605 | C2 | semidirect |
| 5. #26041533 | C2 | semidirect |
| 6. #26041475 | C2 | semidirect |
| 7. #26041414 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. #26041356 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 14. C2×D1448 | C22 | semidirect |
| 16. C2×#15668432 | C22 | semidirect |
| 21. #19153791 | C22 | semidirect |
| 25. C4×D724 | C22 | semidirect |
| 27. #19153774 | C22 | semidirect |
| 28. #19153749 | C22 | semidirect |
| 29. #19153738 | C22 | semidirect |
| 31. #19153736 | C22 | semidirect |
| 32. #19153736 | C22 | semidirect |
| 33. #19153736 | C22 | semidirect |
| 34. #19153728 | C22 | semidirect |
| 35. C4×#13089678 | C22 | semidirect |
| 36. C4⋊Q8×C181 | C22 | semidirect |
| 38. #106×C181 | C22 | semidirect |
| 39. C4⋊C8×C181 | C22 | semidirect |
| 140. C181 | #3325 | semidirect |
| 146. #476 | D181 | semidirect |
| 158. C4⋊Q8 | C2×D181 | semidirect |
| 172. #106 | C2×D181 | semidirect |
| 173. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041995 | 2 |
| D4×D724 | 2 |
| #26041627 | 2 |
| #26041605 | 2 |
| #26041533 | 2 |
| #26041475 | 2 |
| #26041414 | 2 |
| C4×#15668434 | 2 |
| #26041356 | 2 |
| #26041282 | 2 |
| #476×C181 | 2 |
| #3325 | 181 |