Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153835 | C2 | semidirect |
| 2. C22×C8×D181 | C2 | semidirect |
| 3. #26041789 | C2 | semidirect |
| 4. #26041521 | C2 | semidirect |
| 5. #26041520 | C2 | semidirect |
| 6. #26041512 | C2 | semidirect |
| 7. #26041507 | C2 | semidirect |
| 8. #26041506 | C2 | semidirect |
| 9. #26041316 | C2 | semidirect |
| 10. #26041272 | C2 | semidirect |
| 11. #466×C181 | C2 | semidirect |
| 15. C2×Dic724 | C22 | semidirect |
| 16. C2×#15668437 | C22 | semidirect |
| 31. #19153750 | C22 | semidirect |
| 32. #19153747 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 35. #19153737 | C22 | semidirect |
| 36. C2×D8×C181 | C22 | semidirect |
| 39. #107×C181 | C22 | semidirect |
| 40. #102×C181 | C22 | semidirect |
| 63. C8×D181 | D4 | semidirect |
| 121. C22×C181 | #135 | semidirect |
| 129. C2×D181 | #135 | semidirect |
| 145. C181 | #3050 | semidirect |
| 153. #466 | D181 | semidirect |
| 163. C2×D8 | C2×D181 | semidirect |
| 181. #107 | C2×D181 | semidirect |
| 186. #102 | C2×D181 | semidirect |
| 274. C22 | #19153835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153835 | 2 |
| C22×C8×D181 | 2 |
| #26041789 | 2 |
| #26041521 | 2 |
| #26041520 | 2 |
| #26041512 | 2 |
| #26041507 | 2 |
| #26041506 | 2 |
| #26041316 | 2 |
| #26041272 | 2 |
| #466×C181 | 2 |
| #3050 | 181 |