Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27133214 | C2 | semidirect |
| 2. #127×D191 | C2 | semidirect |
| 3. #27133040 | C2 | semidirect |
| 4. #27133039 | C2 | semidirect |
| 5. #27133011 | C2 | semidirect |
| 6. #27132857 | C2 | semidirect |
| 7. #27132798 | C2 | semidirect |
| 8. #27132714 | C2 | semidirect |
| 9. #486×C191 | C2 | semidirect |
| 14. C2×D1528 | C22 | semidirect |
| 15. C2×#15690272 | C22 | semidirect |
| 17. #20259319 | C22 | semidirect |
| 25. #20259284 | C22 | semidirect |
| 27. Dic191⋊C8 | C22 | semidirect |
| 28. #20259242 | C22 | semidirect |
| 30. C4×C191⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C191 | C22 | semidirect |
| 33. #102×C191 | C22 | semidirect |
| 34. C4×C8×C191 | C22 | semidirect |
| 92. C4×D191 | D8 | semidirect |
| 132. C191 | #3205 | semidirect |
| 139. #486 | D191 | semidirect |
| 149. C4⋊Q8 | C2×D191 | semidirect |
| 164. #102 | C2×D191 | semidirect |
| 167. C4×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133214 | 2 |
| #127×D191 | 2 |
| #27133040 | 2 |
| #27133039 | 2 |
| #27133011 | 2 |
| #27132857 | 2 |
| #27132798 | 2 |
| #27132714 | 2 |
| #486×C191 | 2 |
| #3205 | 191 |