Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#20259349 | C2 | semidirect |
| 2. #27133214 | C2 | semidirect |
| 3. #127×D191 | C2 | semidirect |
| 4. #27133049 | C2 | semidirect |
| 5. #27133040 | C2 | semidirect |
| 6. #27133039 | C2 | semidirect |
| 7. #27133037 | C2 | semidirect |
| 8. C4×#15690270 | C2 | semidirect |
| 9. #492×C191 | C2 | semidirect |
| 14. C2×#15690274 | C22 | semidirect |
| 15. C2×D1528 | C22 | semidirect |
| 16. C2×#15690272 | C22 | semidirect |
| 19. #20259319 | C22 | semidirect |
| 22. #20259311 | C22 | semidirect |
| 26. #20259232 | C22 | semidirect |
| 27. C4×C191⋊C8 | C22 | semidirect |
| 28. C2×SD16×C191 | C22 | semidirect |
| 29. C4⋊Q8×C191 | C22 | semidirect |
| 31. C4×C8×C191 | C22 | semidirect |
| 49. #15690270 | D4 | semidirect |
| 78. C191⋊C8 | C2×D4 | semidirect |
| 86. C8×C191 | C2×D4 | semidirect |
| 98. C4×C191 | AGL(1,ℤ/8) | semidirect |
| 108. C191 | #3151 | semidirect |
| 117. #492 | D191 | semidirect |
| 124. C2×SD16 | C2×D191 | semidirect |
| 128. C4⋊Q8 | C2×D191 | semidirect |
| 140. C4×C8 | C2×D191 | semidirect |
| 195. C8 | D4×D191 | semidirect |
| 209. C4 | #20259349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259349 | 2 |
| #27133214 | 2 |
| #127×D191 | 2 |
| #27133049 | 2 |
| #27133040 | 2 |
| #27133039 | 2 |
| #27133037 | 2 |
| C4×#15690270 | 2 |
| #492×C191 | 2 |
| #3151 | 191 |