Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 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. #26042002 | C2 | semidirect |
| 3. #26041625 | C2 | semidirect |
| 4. #26041601 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041522 | C2 | semidirect |
| 7. #26041428 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. #26041356 | C2 | semidirect |
| 10. #26041282 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 15. C2×#15668432 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 19. #19153792 | C22 | semidirect |
| 26. #19153774 | C22 | semidirect |
| 27. #19153750 | C22 | semidirect |
| 28. #19153747 | C22 | semidirect |
| 29. #19153740 | C22 | semidirect |
| 31. #19153737 | C22 | semidirect |
| 32. #19153737 | C22 | semidirect |
| 34. #19153728 | C22 | semidirect |
| 35. C4×#13089678 | C22 | semidirect |
| 36. C2×SD16×C181 | C22 | semidirect |
| 38. C4×Q8×C181 | C22 | semidirect |
| 39. C4⋊C8×C181 | C22 | semidirect |
| 40. #102×C181 | C22 | semidirect |
| 135. C181 | #3324 | semidirect |
| 143. #460 | D181 | semidirect |
| 151. C2×SD16 | C2×D181 | semidirect |
| 162. C4×Q8 | C2×D181 | semidirect |
| 168. C4⋊C8 | C2×D181 | semidirect |
| 174. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041914 | 2 |
| #26041625 | 2 |
| #26041601 | 2 |
| #26041560 | 2 |
| #26041522 | 2 |
| #26041428 | 2 |
| C4×#15668436 | 2 |
| #26041356 | 2 |
| #26041282 | 2 |
| #460×C181 | 2 |
| #3324 | 181 |