Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #26042242 | C2 | semidirect |
| 4. C2×C8×#10624382 | C2 | semidirect |
| 5. #26042154 | C2 | semidirect |
| 6. #26042151 | C2 | semidirect |
| 12. #19153881 | C4 | semidirect |
| 13. #19153880 | C4 | semidirect |
| 14. #19153879 | C4 | semidirect |
| 15. #19153878 | C4 | semidirect |
| 22. #19153824 | C4 | semidirect |
| 23. #19153823 | C4 | semidirect |
| 25. #19153822 | C4 | semidirect |
| 30. #131×C181 | C4 | semidirect |
| 127. C181 | #1764 | semidirect |
| 142. #131 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊#104 | 2 |
| #26042269 | 2 |
| #26042242 | 2 |
| C2×C8×#10624382 | 2 |
| #26042154 | 2 |
| #26042151 | 2 |
| #131×D181 | 2 |
| #1764 | 181 |