Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26041832 | C2 | semidirect |
| 3. #26041642 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041285 | C2 | semidirect |
| 6. #26041284 | C2 | semidirect |
| 7. #26041283 | C2 | semidirect |
| 8. M16×Dic181 | C2 | semidirect |
| 9. #418×C181 | C2 | semidirect |
| 13. #19153815 | C22 | semidirect |
| 17. #19153807 | C22 | semidirect |
| 22. #19153738 | C22 | semidirect |
| 23. #19153737 | C22 | semidirect |
| 24. #19153736 | C22 | semidirect |
| 25. #19153726 | C22 | semidirect |
| 26. C8×Dic181 | C22 | semidirect |
| 30. #102×C181 | C22 | semidirect |
| 111. C181 | #3138 | semidirect |
| 120. #418 | D181 | semidirect |
| 140. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| C2×#19153812 | 2 |
| #26041642 | 2 |
| #26041624 | 2 |
| #26041285 | 2 |
| #26041284 | 2 |
| #26041283 | 2 |
| M16×Dic181 | 2 |
| #418×C181 | 2 |
| #3138 | 181 |