Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153847 | C2 | semidirect |
| 2. C2×#19153842 | C2 | semidirect |
| 3. C2×#19153838 | C2 | semidirect |
| 4. #26041853 | C2 | semidirect |
| 5. #26041846 | C2 | semidirect |
| 6. #26041670 | C2 | semidirect |
| 7. #26041665 | C2 | semidirect |
| 8. #26041660 | C2 | semidirect |
| 9. #26041650 | C2 | semidirect |
| 10. #26041234 | C2 | semidirect |
| 11. C22×SD16×C181 | C2 | semidirect |
| 17. C2×Dic724 | C22 | semidirect |
| 18. C2×#15668439 | C22 | semidirect |
| 19. C2×#15668438 | C22 | semidirect |
| 20. C2×#15668438 | C22 | semidirect |
| 22. C2×#15668436 | C22 | semidirect |
| 23. C2×D1448 | C22 | semidirect |
| 26. #19153814 | C22 | semidirect |
| 28. #19153805 | C22 | semidirect |
| 35. #19153726 | C22 | semidirect |
| 36. C8×Dic181 | C22 | semidirect |
| 64. #15668433 | D4 | semidirect |
| 85. C2×C8×C181 | D4 | semidirect |
| 148. C181 | #3154 | semidirect |
| 153. C22×SD16 | D181 | semidirect |
| 228. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C2×#19153842 | 2 |
| C2×#19153838 | 2 |
| #26041853 | 2 |
| #26041846 | 2 |
| #26041670 | 2 |
| #26041665 | 2 |
| #26041660 | 2 |
| #26041650 | 2 |
| #26041234 | 2 |
| C22×SD16×C181 | 2 |
| #3154 | 181 |