Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 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. #26041836 | C2 | semidirect |
| 3. #26041615 | C2 | semidirect |
| 4. #26041560 | C2 | semidirect |
| 5. #26041485 | C2 | semidirect |
| 7. #26041381 | C2 | semidirect |
| 8. #432×C181 | C2 | semidirect |
| 12. #19153816 | C22 | semidirect |
| 13. #19153816 | C22 | semidirect |
| 18. C4×Dic362 | C22 | semidirect |
| 26. #19153750 | C22 | semidirect |
| 27. #19153741 | C22 | semidirect |
| 30. C4⋊C8×C181 | C22 | semidirect |
| 32. #97×C181 | C22 | semidirect |
| 112. C181 | #3110 | semidirect |
| 121. #432 | D181 | semidirect |
| 141. C4⋊C8 | C2×D181 | semidirect |
| 145. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| C2×C4×D724 | 2 |
| #26041615 | 2 |
| #26041560 | 2 |
| #26041485 | 2 |
| #26041432 | 2 |
| #26041381 | 2 |
| #432×C181 | 2 |
| #3110 | 181 |