Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×#19153774 | C2 | semidirect |
| 3. #26041605 | C2 | semidirect |
| 4. #26041601 | C2 | semidirect |
| 5. #26041597 | C2 | semidirect |
| 6. #26041593 | C2 | semidirect |
| 7. #26041590 | C2 | semidirect |
| 8. #26041318 | C2 | semidirect |
| 9. #26041282 | C2 | semidirect |
| 10. #26041241 | C2 | semidirect |
| 11. #481×C181 | C2 | semidirect |
| 24. #19153774 | C22 | semidirect |
| 25. C2×C4⋊Dic181 | C22 | semidirect |
| 30. #19153750 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153747 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153737 | C22 | semidirect |
| 35. #19153736 | C22 | semidirect |
| 36. C22⋊#13089678 | C22 | semidirect |
| 37. #19153728 | C22 | semidirect |
| 39. C2×C4⋊C4×C181 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 41. #102×C181 | C22 | semidirect |
| 42. C22⋊C8×C181 | C22 | semidirect |
| 153. C181 | #3094 | semidirect |
| 160. #481 | D181 | semidirect |
| 182. C2×C4⋊C4 | C2×D181 | semidirect |
| 189. #106 | C2×D181 | semidirect |
| 193. #102 | C2×D181 | semidirect |
| 196. C22⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D181 | 2 |
| C2×#19153774 | 2 |
| #26041605 | 2 |
| #26041601 | 2 |
| #26041597 | 2 |
| #26041593 | 2 |
| #26041590 | 2 |
| #26041318 | 2 |
| #26041282 | 2 |
| #26041241 | 2 |
| #481×C181 | 2 |
| #3094 | 181 |