Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26041674 | C2 | semidirect |
| 4. #26041673 | C2 | semidirect |
| 5. #26041641 | C2 | semidirect |
| 6. #26041504 | C2 | semidirect |
| 7. #26041500 | C2 | semidirect |
| 8. #26041436 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #489×C181 | C2 | semidirect |
| 14. C2×Dic724 | C22 | semidirect |
| 15. C2×#15668439 | C22 | semidirect |
| 18. #19153816 | C22 | semidirect |
| 28. #19153781 | C22 | semidirect |
| 33. #19153745 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 37. #19153727 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #103×C181 | C22 | semidirect |
| 42. #97×C181 | C22 | semidirect |
| 142. C181 | #3215 | semidirect |
| 149. #489 | D181 | semidirect |
| 162. C4⋊Q8 | C2×D181 | semidirect |
| 180. #103 | C2×D181 | semidirect |
| 185. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #124×D181 | 2 |
| #26041674 | 2 |
| #26041673 | 2 |
| #26041641 | 2 |
| #26041504 | 2 |
| #26041500 | 2 |
| #26041436 | 2 |
| #26041431 | 2 |
| #26041334 | 2 |
| #489×C181 | 2 |
| #3215 | 181 |