Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#15690272 | C2 | semidirect |
| 2. #27133227 | C2 | semidirect |
| 3. #27133138 | C2 | semidirect |
| 4. #27132880 | C2 | semidirect |
| 5. #27132856 | C2 | semidirect |
| 6. #27132691 | C2 | semidirect |
| 7. #27132669 | C2 | semidirect |
| 8. #27132659 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C191 | C2 | semidirect |
| 14. #20259318 | C22 | semidirect |
| 15. #20259311 | C22 | semidirect |
| 19. D4×Dic191 | C22 | semidirect |
| 23. Dic191⋊C8 | C22 | semidirect |
| 24. #20259246 | C22 | semidirect |
| 25. #20259244 | C22 | semidirect |
| 26. #20259243 | C22 | semidirect |
| 30. C2×SD16×C191 | C22 | semidirect |
| 31. C2×D8×C191 | C22 | semidirect |
| 58. C2×D4×C191 | D4 | semidirect |
| 121. C191 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D191 | semidirect |
| 136. C2×SD16 | C2×D191 | semidirect |
| 139. C2×D8 | C2×D191 | semidirect |
| 168. C2×D4 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690272 | 2 |
| #27133227 | 2 |
| #27133138 | 2 |
| #27132880 | 2 |
| #27132856 | 2 |
| #27132691 | 2 |
| #27132669 | 2 |
| #27132659 | 2 |
| C2×AGL(1,ℤ/8)×C191 | 2 |
| #3041 | 191 |