Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26041830 | C2 | semidirect |
| 2. #124×D181 | C2 | semidirect |
| 3. #26041669 | C2 | semidirect |
| 4. #26041668 | C2 | semidirect |
| 5. #26041641 | C2 | semidirect |
| 6. #26041497 | C2 | semidirect |
| 7. #26041493 | C2 | semidirect |
| 8. #26041419 | C2 | semidirect |
| 9. #26041414 | C2 | semidirect |
| 10. #26041334 | C2 | semidirect |
| 11. #489×C181 | C2 | semidirect |
| 15. C2×#15668438 | C22 | semidirect |
| 16. C2×#15668436 | C22 | semidirect |
| 19. #19153813 | C22 | semidirect |
| 29. #19153778 | C22 | semidirect |
| 33. #19153745 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 37. #19153727 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #103×C181 | C22 | semidirect |
| 42. #97×C181 | C22 | semidirect |
| 150. C181 | #3213 | semidirect |
| 157. #489 | D181 | semidirect |
| 170. C4⋊Q8 | C2×D181 | semidirect |
| 188. #103 | C2×D181 | semidirect |
| 193. #97 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041830 | 2 |
| #124×D181 | 2 |
| #26041669 | 2 |
| #26041668 | 2 |
| #26041641 | 2 |
| #26041497 | 2 |
| #26041493 | 2 |
| #26041419 | 2 |
| #26041414 | 2 |
| #26041334 | 2 |
| #489×C181 | 2 |
| #3213 | 181 |