Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#20259296 | C2 | semidirect |
| 2. #27132996 | C2 | semidirect |
| 3. #27132987 | C2 | semidirect |
| 4. #27132979 | C2 | semidirect |
| 5. #27132897 | C2 | semidirect |
| 6. #27132894 | C2 | semidirect |
| 7. #27132813 | C2 | semidirect |
| 8. #27132808 | C2 | semidirect |
| 9. #27132796 | C2 | semidirect |
| 10. C2×C22⋊(C191⋊C8) | C2 | semidirect |
| 11. #525×C191 | C2 | semidirect |
| 14. C2×#15690274 | C22 | semidirect |
| 15. C2×#15690272 | C22 | semidirect |
| 16. C22×C191⋊C8 | C22 | semidirect |
| 23. #20259255 | C22 | semidirect |
| 24. #20259253 | C22 | semidirect |
| 25. #20259246 | C22 | semidirect |
| 26. #20259243 | C22 | semidirect |
| 27. #20259242 | C22 | semidirect |
| 28. #20259242 | C22 | semidirect |
| 31. C22⋊(C191⋊C8) | C22 | semidirect |
| 32. C2×#41×C191 | C22 | semidirect |
| 36. C22⋊Q8×C191 | C22 | semidirect |
| 38. #121×C191 | C22 | semidirect |
| 42. #117×C191 | C22 | semidirect |
| 158. C191 | #3188 | semidirect |
| 160. #525 | D191 | semidirect |
| 171. C2×#41 | C2×D191 | semidirect |
| 180. C22⋊Q8 | C2×D191 | semidirect |
| 186. #121 | C2×D191 | semidirect |
| 190. #117 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259296 | 2 |
| #27132996 | 2 |
| #27132987 | 2 |
| #27132979 | 2 |
| #27132897 | 2 |
| #27132894 | 2 |
| #27132813 | 2 |
| #27132808 | 2 |
| #27132796 | 2 |
| C2×C22⋊(C191⋊C8) | 2 |
| #525×C191 | 2 |
| #3188 | 191 |