Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #27133461 | C2 | semidirect |
| 2. C2×#20259348 | C2 | semidirect |
| 3. #27133429 | C2 | semidirect |
| 4. #27132930 | C2 | semidirect |
| 5. #27132923 | C2 | semidirect |
| 6. #27132712 | C2 | semidirect |
| 7. #27132647 | C2 | semidirect |
| 8. C2×#20259239 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C191 | C2 | semidirect |
| 11. #20259353 | C22 | semidirect |
| 15. #20259348 | C22 | semidirect |
| 21. #20259328 | C22 | semidirect |
| 26. #20259258 | C22 | semidirect |
| 27. #20259241 | C22 | semidirect |
| 28. #20259239 | C22 | semidirect |
| 29. #20259239 | C22 | semidirect |
| 34. C2×SD16×C191 | C22 | semidirect |
| 35. C2×D8×C191 | C22 | semidirect |
| 147. C191 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D191 | semidirect |
| 171. C2×SD16 | C2×D191 | semidirect |
| 173. C2×D8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133461 | 2 |
| C2×#20259348 | 2 |
| #27133429 | 2 |
| #27132930 | 2 |
| #27132923 | 2 |
| #27132712 | 2 |
| #27132647 | 2 |
| C2×#20259239 | 2 |
| C2×AGL(1,ℤ/8)×C191 | 2 |
| #3068 | 191 |