Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 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×#20259348 | C2 | semidirect |
| 2. C22×#15690272 | C2 | semidirect |
| 3. #27133232 | C2 | semidirect |
| 4. #27132878 | C2 | semidirect |
| 5. #27132858 | C2 | semidirect |
| 6. #27132690 | C2 | semidirect |
| 7. #27132667 | C2 | semidirect |
| 8. #27132657 | C2 | semidirect |
| 9. #518×C191 | C2 | semidirect |
| 13. C2×#15690275 | C22 | semidirect |
| 16. C2×#15690272 | C22 | semidirect |
| 19. #20259319 | C22 | semidirect |
| 20. #20259310 | C22 | semidirect |
| 23. C4⋊(C191⋊C8) | C22 | semidirect |
| 24. #20259245 | C22 | semidirect |
| 25. #20259242 | C22 | semidirect |
| 26. #20259242 | C22 | semidirect |
| 29. C4×D4×C191 | C22 | semidirect |
| 56. C2×D4×C191 | D4 | semidirect |
| 121. C191 | #3041 | semidirect |
| 126. #518 | D191 | semidirect |
| 147. C4×D4 | C2×D191 | semidirect |
| 169. C2×D4 | D764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259348 | 2 |
| C22×#15690272 | 2 |
| #27133232 | 2 |
| #27132878 | 2 |
| #27132858 | 2 |
| #27132690 | 2 |
| #27132667 | 2 |
| #27132657 | 2 |
| #518×C191 | 2 |
| #3041 | 191 |