Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27133227 | C2 | semidirect |
| 2. #27132987 | C2 | semidirect |
| 3. #27132984 | C2 | semidirect |
| 4. #27132914 | C2 | semidirect |
| 5. #27132897 | C2 | semidirect |
| 6. #27132797 | C2 | semidirect |
| 7. #27132796 | C2 | semidirect |
| 8. #27132630 | C2 | semidirect |
| 9. #535×C191 | C2 | semidirect |
| 10. C22×D764 | C22 | semidirect |
| 13. C2×#15690271 | C22 | semidirect |
| 14. C22×C191⋊C8 | C22 | semidirect |
| 18. #20259296 | C22 | semidirect |
| 21. #20259281 | C22 | semidirect |
| 22. #20259255 | C22 | semidirect |
| 23. #20259253 | C22 | semidirect |
| 24. #20259243 | C22 | semidirect |
| 25. #20259243 | C22 | semidirect |
| 26. #20259242 | C22 | semidirect |
| 27. #20259242 | C22 | semidirect |
| 28. C22⋊(C191⋊C8) | C22 | semidirect |
| 29. C22⋊(C191⋊C8) | C22 | semidirect |
| 31. C22×D4×C191 | C22 | semidirect |
| 35. #121×C191 | C22 | semidirect |
| 38. #117×C191 | C22 | semidirect |
| 144. C191 | #3199 | semidirect |
| 147. #535 | D191 | semidirect |
| 157. C22×D4 | C2×D191 | semidirect |
| 169. #121 | C2×D191 | semidirect |
| 175. #117 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133227 | 2 |
| #27132987 | 2 |
| #27132984 | 2 |
| #27132914 | 2 |
| #27132897 | 2 |
| #27132797 | 2 |
| #27132796 | 2 |
| #27132630 | 2 |
| #535×C191 | 2 |
| #3199 | 191 |