Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 460 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. #26041994 | C2 | semidirect |
| 2. #26041914 | C2 | semidirect |
| 3. #26041625 | C2 | semidirect |
| 4. #26041602 | C2 | semidirect |
| 5. #26041570 | C2 | semidirect |
| 6. #26041529 | C2 | semidirect |
| 7. #26041411 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. #26041356 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. #459×C181 | C2 | semidirect |
| 15. C2×#15668432 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 21. #19153787 | C22 | semidirect |
| 26. #19153774 | C22 | semidirect |
| 27. #19153749 | C22 | semidirect |
| 28. #19153748 | C22 | semidirect |
| 30. #19153737 | C22 | semidirect |
| 31. #19153737 | C22 | semidirect |
| 32. #19153737 | C22 | semidirect |
| 34. #19153728 | C22 | semidirect |
| 35. C4×#13089678 | C22 | semidirect |
| 36. C2×D8×C181 | C22 | semidirect |
| 38. C4×D4×C181 | C22 | semidirect |
| 39. C4⋊C8×C181 | C22 | semidirect |
| 40. #102×C181 | C22 | semidirect |
| 140. C181 | #3325 | semidirect |
| 148. #459 | D181 | semidirect |
| 156. C2×D8 | C2×D181 | semidirect |
| 168. C4×D4 | C2×D181 | semidirect |
| 173. C4⋊C8 | C2×D181 | semidirect |
| 179. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| #26041914 | 2 |
| #26041625 | 2 |
| #26041602 | 2 |
| #26041570 | 2 |
| #26041529 | 2 |
| #26041411 | 2 |
| C4×#15668434 | 2 |
| #26041356 | 2 |
| #26041282 | 2 |
| #459×C181 | 2 |
| #3325 | 181 |