Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26041834 | C2 | semidirect |
| 3. #26041578 | C2 | semidirect |
| 4. #26041577 | C2 | semidirect |
| 5. #26041566 | C2 | semidirect |
| 6. #26041560 | C2 | semidirect |
| 7. #26041559 | C2 | semidirect |
| 8. #26041318 | C2 | semidirect |
| 9. #26041301 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 15. #19153816 | C22 | semidirect |
| 16. #19153807 | C22 | semidirect |
| 30. #19153750 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153747 | C22 | semidirect |
| 33. C4⋊#13089678 | C22 | semidirect |
| 34. #19153745 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 48. D4×D181 | Q8 | semidirect |
| 144. C181 | #3077 | semidirect |
| 151. #476 | D181 | semidirect |
| 161. C4⋊Q8 | C2×D181 | semidirect |
| 180. #106 | C2×D181 | semidirect |
| 183. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| C4×D4×D181 | 2 |
| #26041578 | 2 |
| #26041577 | 2 |
| #26041566 | 2 |
| #26041560 | 2 |
| #26041559 | 2 |
| #26041318 | 2 |
| #26041301 | 2 |
| #26041282 | 2 |
| #476×C181 | 2 |
| #3077 | 181 |