Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#15690276 | C2 | semidirect |
| 3. #27133239 | C2 | semidirect |
| 4. #27133137 | C2 | semidirect |
| 5. #27132879 | C2 | semidirect |
| 6. #27132869 | C2 | semidirect |
| 7. #27132673 | C2 | semidirect |
| 8. #27132660 | C2 | semidirect |
| 9. #424×C191 | C2 | semidirect |
| 18. #20259322 | C22 | semidirect |
| 19. #20259310 | C22 | semidirect |
| 26. #20259247 | C22 | semidirect |
| 27. #20259247 | C22 | semidirect |
| 28. #20259244 | C22 | semidirect |
| 32. C4⋊C8×C191 | C22 | semidirect |
| 116. C191 | #3042 | semidirect |
| 124. #424 | D191 | semidirect |
| 146. C4⋊C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259350 | 2 |
| C22×#15690276 | 2 |
| #27133239 | 2 |
| #27133137 | 2 |
| #27132879 | 2 |
| #27132869 | 2 |
| #27132673 | 2 |
| #27132660 | 2 |
| #424×C191 | 2 |
| #3042 | 191 |