Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041826 | C2 | semidirect |
| 2. #127×D181 | C2 | semidirect |
| 3. #26041654 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041475 | C2 | semidirect |
| 6. #26041474 | C2 | semidirect |
| 7. #26041471 | C2 | semidirect |
| 8. #26041414 | C2 | semidirect |
| 9. #26041411 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #459×C181 | C2 | semidirect |
| 16. C2×D1448 | C22 | semidirect |
| 17. C2×#15668434 | C22 | semidirect |
| 18. C2×#15668434 | C22 | semidirect |
| 19. #19153815 | C22 | semidirect |
| 24. #19153812 | 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. C8×Dic181 | C22 | semidirect |
| 38. C2×D8×C181 | C22 | semidirect |
| 40. C4×D4×C181 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 42. #102×C181 | C22 | semidirect |
| 115. C4×D181 | D8 | semidirect |
| 165. C181 | #3205 | semidirect |
| 174. #459 | D181 | semidirect |
| 185. C2×D8 | C2×D181 | semidirect |
| 199. C4×D4 | C2×D181 | semidirect |
| 202. C4⋊C8 | C2×D181 | semidirect |
| 206. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041826 | 2 |
| #127×D181 | 2 |
| #26041654 | 2 |
| #26041624 | 2 |
| #26041475 | 2 |
| #26041474 | 2 |
| #26041471 | 2 |
| #26041414 | 2 |
| #26041411 | 2 |
| #26041331 | 2 |
| #459×C181 | 2 |
| #3205 | 181 |