Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153844 | C2 | semidirect |
| 2. C2×#19153838 | C2 | semidirect |
| 3. #26041848 | C2 | semidirect |
| 4. #26041759 | C2 | semidirect |
| 5. #26041502 | C2 | semidirect |
| 6. #26041495 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041475 | C2 | semidirect |
| 9. #26041281 | C2 | semidirect |
| 10. C2×#19153738 | C2 | semidirect |
| 11. #424×C181 | C2 | semidirect |
| 17. C2×Dic724 | C22 | semidirect |
| 19. C2×#15668438 | C22 | semidirect |
| 20. C2×#15668438 | C22 | semidirect |
| 22. C2×D1448 | C22 | semidirect |
| 28. C4×Dic362 | C22 | semidirect |
| 29. C4×D724 | C22 | semidirect |
| 34. #19153741 | C22 | semidirect |
| 37. #19153738 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 42. C4⋊C8×C181 | C22 | semidirect |
| 47. #15668449 | D4 | semidirect |
| 154. C181 | #3045 | semidirect |
| 164. #424 | D181 | semidirect |
| 192. C4⋊C8 | C2×D181 | semidirect |
| 193. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| C2×#19153838 | 2 |
| #26041848 | 2 |
| #26041759 | 2 |
| #26041502 | 2 |
| #26041495 | 2 |
| #26041480 | 2 |
| #26041475 | 2 |
| #26041281 | 2 |
| C2×#19153738 | 2 |
| #424×C181 | 2 |
| #3045 | 181 |