Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26041623 | C2 | semidirect |
| 4. #26041622 | C2 | semidirect |
| 5. #26041616 | C2 | semidirect |
| 6. #26041611 | C2 | semidirect |
| 7. #26041319 | C2 | semidirect |
| 8. #26041289 | C2 | semidirect |
| 9. #26041287 | C2 | semidirect |
| 11. #428×C181 | C2 | semidirect |
| 30. #19153749 | C22 | semidirect |
| 31. #19153747 | C22 | semidirect |
| 32. #19153741 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 35. #19153739 | C22 | semidirect |
| 41. #107×C181 | C22 | semidirect |
| 42. #106×C181 | C22 | semidirect |
| 146. C181 | #3095 | semidirect |
| 155. #428 | D181 | semidirect |
| 181. #107 | C2×D181 | semidirect |
| 183. #106 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153796 | 2 |
| #117×D181 | 2 |
| #26041623 | 2 |
| #26041622 | 2 |
| #26041616 | 2 |
| #26041611 | 2 |
| #26041319 | 2 |
| #26041289 | 2 |
| #26041287 | 2 |
| #26041242 | 2 |
| #428×C181 | 2 |
| #3095 | 181 |