Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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×#19153841 | C2 | semidirect |
| 2. C22×D1448 | C2 | semidirect |
| 3. #26041843 | C2 | semidirect |
| 4. #26041753 | C2 | semidirect |
| 5. #26041497 | C2 | semidirect |
| 6. #26041473 | C2 | semidirect |
| 7. #26041305 | C2 | semidirect |
| 8. #26041283 | C2 | semidirect |
| 9. #416×C181 | C2 | semidirect |
| 13. C2×#15668436 | C22 | semidirect |
| 16. C2×#15668434 | C22 | semidirect |
| 18. #19153812 | C22 | semidirect |
| 19. #19153805 | C22 | semidirect |
| 23. #19153778 | C22 | semidirect |
| 26. #19153745 | C22 | semidirect |
| 27. #19153736 | C22 | semidirect |
| 31. #103×C181 | C22 | semidirect |
| 32. #102×C181 | C22 | semidirect |
| 40. C2×D724 | D4 | semidirect |
| 121. C181 | #3041 | semidirect |
| 131. #416 | D181 | semidirect |
| 152. #103 | C2×D181 | semidirect |
| 154. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C22×D1448 | 2 |
| #26041843 | 2 |
| #26041753 | 2 |
| #26041497 | 2 |
| #26041473 | 2 |
| #26041305 | 2 |
| #26041283 | 2 |
| #416×C181 | 2 |
| #3041 | 181 |