Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 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. #127×D181 | C2 | semidirect |
| 2. #26041816 | C2 | semidirect |
| 3. #26041665 | C2 | semidirect |
| 4. #26041642 | C2 | semidirect |
| 5. #26041479 | C2 | semidirect |
| 6. #26041475 | C2 | semidirect |
| 7. #26041471 | C2 | semidirect |
| 8. #26041428 | C2 | semidirect |
| 9. #26041414 | C2 | semidirect |
| 10. #26041335 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 15. C2×#15668436 | C22 | semidirect |
| 16. C2×D1448 | C22 | semidirect |
| 17. C2×#15668434 | C22 | semidirect |
| 23. #19153807 | C22 | semidirect |
| 24. #19153805 | C22 | semidirect |
| 29. C4×D724 | C22 | semidirect |
| 32. C4⋊#13089678 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153737 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 38. C2×SD16×C181 | C22 | semidirect |
| 40. C4×Q8×C181 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 42. #102×C181 | C22 | semidirect |
| 156. C181 | #3217 | semidirect |
| 163. #460 | D181 | semidirect |
| 173. C2×SD16 | C2×D181 | semidirect |
| 187. C4×Q8 | C2×D181 | semidirect |
| 193. C4⋊C8 | C2×D181 | semidirect |
| 197. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D181 | 2 |
| #26041816 | 2 |
| #26041665 | 2 |
| #26041642 | 2 |
| #26041479 | 2 |
| #26041475 | 2 |
| #26041471 | 2 |
| #26041428 | 2 |
| #26041414 | 2 |
| #26041335 | 2 |
| #460×C181 | 2 |
| #3217 | 181 |