Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×#19153774 | C2 | semidirect |
| 3. #26041623 | C2 | semidirect |
| 4. #26041614 | C2 | semidirect |
| 5. #26041610 | C2 | semidirect |
| 6. #26041602 | C2 | semidirect |
| 7. #26041590 | C2 | semidirect |
| 8. #26041314 | C2 | semidirect |
| 9. #26041272 | C2 | semidirect |
| 10. C22⋊C8×D181 | C2 | semidirect |
| 11. #481×C181 | C2 | semidirect |
| 30. #19153749 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153748 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 35. #19153737 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 41. #102×C181 | C22 | semidirect |
| 143. C181 | #3091 | semidirect |
| 151. #481 | D181 | semidirect |
| 179. #106 | C2×D181 | semidirect |
| 183. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041789 | 2 |
| C2×#19153774 | 2 |
| #26041623 | 2 |
| #26041614 | 2 |
| #26041610 | 2 |
| #26041602 | 2 |
| #26041590 | 2 |
| #26041314 | 2 |
| #26041272 | 2 |
| C22⋊C8×D181 | 2 |
| #481×C181 | 2 |
| #3091 | 181 |