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×#20259330 | C2 | semidirect |
| 2. #27133241 | C2 | semidirect |
| 3. #27133230 | C2 | semidirect |
| 4. #27132913 | C2 | semidirect |
| 5. #27132906 | C2 | semidirect |
| 6. #27132896 | C2 | semidirect |
| 7. #27132889 | C2 | semidirect |
| 8. #27132705 | C2 | semidirect |
| 9. #27132659 | C2 | semidirect |
| 10. C2×#20259243 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C191 | C2 | semidirect |
| 14. C2×#15690270 | C22 | semidirect |
| 16. C2×C8×D191 | C22 | semidirect |
| 20. #20259298 | C22 | semidirect |
| 25. #20259293 | C22 | semidirect |
| 29. #20259256 | C22 | semidirect |
| 30. #20259254 | C22 | semidirect |
| 31. #20259246 | C22 | semidirect |
| 32. #20259246 | C22 | semidirect |
| 35. #20259243 | C22 | semidirect |
| 36. #20259243 | C22 | semidirect |
| 83. M16×C191 | D4 | semidirect |
| 151. C191 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D191 | semidirect |
| 220. M16 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259330 | 2 |
| #27133241 | 2 |
| #27133230 | 2 |
| #27132913 | 2 |
| #27132906 | 2 |
| #27132896 | 2 |
| #27132889 | 2 |
| #27132705 | 2 |
| #27132659 | 2 |
| C2×#20259243 | 2 |
| C2×AGL(1,ℤ/8)×C191 | 2 |
| #3062 | 191 |