Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
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×#20259348 | C2 | semidirect |
| 2. C2×#20259329 | C2 | semidirect |
| 3. #27133241 | C2 | semidirect |
| 4. #27132914 | C2 | semidirect |
| 5. #27132907 | C2 | semidirect |
| 6. #27132897 | C2 | semidirect |
| 7. #27132890 | C2 | semidirect |
| 8. #27132706 | C2 | semidirect |
| 9. #27132657 | C2 | semidirect |
| 10. C2×#20259243 | C2 | semidirect |
| 11. #535×C191 | C2 | semidirect |
| 18. C2×#15690271 | C22 | semidirect |
| 20. C22×C191⋊C8 | C22 | semidirect |
| 21. #20259301 | C22 | semidirect |
| 23. #20259296 | C22 | semidirect |
| 27. #20259255 | C22 | semidirect |
| 28. #20259253 | C22 | semidirect |
| 29. #20259245 | C22 | semidirect |
| 30. #20259245 | C22 | semidirect |
| 33. #20259242 | C22 | semidirect |
| 34. #20259242 | C22 | semidirect |
| 54. #15690271 | D4 | semidirect |
| 151. C191 | #3062 | semidirect |
| 156. #535 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259348 | 2 |
| C2×#20259329 | 2 |
| #27133241 | 2 |
| #27132914 | 2 |
| #27132907 | 2 |
| #27132897 | 2 |
| #27132890 | 2 |
| #27132706 | 2 |
| #27132657 | 2 |
| C2×#20259243 | 2 |
| #535×C191 | 2 |
| #3062 | 191 |