Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041910 | C2 | semidirect |
| 3. #26041642 | C2 | semidirect |
| 4. #26041640 | C2 | semidirect |
| 5. #26041635 | C2 | semidirect |
| 6. #26041624 | C2 | semidirect |
| 7. #26041285 | C2 | semidirect |
| 8. #26041275 | C2 | semidirect |
| 9. C2×#19153736 | C2 | semidirect |
| 10. #26041237 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 15. #19153815 | C22 | semidirect |
| 18. #19153807 | C22 | semidirect |
| 26. #19153740 | C22 | semidirect |
| 27. #19153740 | C22 | semidirect |
| 30. #19153737 | C22 | semidirect |
| 31. #19153737 | C22 | semidirect |
| 34. #19153726 | C22 | semidirect |
| 35. C8×Dic181 | C22 | semidirect |
| 39. #103×C181 | C22 | semidirect |
| 40. #102×C181 | C22 | semidirect |
| 135. C181 | #3136 | semidirect |
| 144. #417 | D181 | semidirect |
| 167. #103 | 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 |
|---|---|
| #26041910 | 2 |
| #26041843 | 2 |
| #26041642 | 2 |
| #26041640 | 2 |
| #26041635 | 2 |
| #26041624 | 2 |
| #26041285 | 2 |
| #26041275 | 2 |
| C2×#19153736 | 2 |
| #26041237 | 2 |
| #417×C181 | 2 |
| #3136 | 181 |