Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #27133144 | C2 | semidirect |
| 3. #27132986 | C2 | semidirect |
| 4. #27132985 | C2 | semidirect |
| 5. #27132980 | C2 | semidirect |
| 6. #27132975 | C2 | semidirect |
| 7. #27132703 | C2 | semidirect |
| 8. #27132701 | C2 | semidirect |
| 9. #27132668 | C2 | semidirect |
| 10. #27132629 | C2 | semidirect |
| 11. C2×#102×C191 | C2 | semidirect |
| 24. #20259280 | C22 | semidirect |
| 25. C4⋊C4×D191 | C22 | semidirect |
| 26. #20259256 | C22 | semidirect |
| 27. #20259256 | C22 | semidirect |
| 28. #20259255 | C22 | semidirect |
| 29. #20259254 | C22 | semidirect |
| 30. #20259254 | C22 | semidirect |
| 31. #20259253 | C22 | semidirect |
| 34. (C2×D191)⋊C8 | C22 | semidirect |
| 35. (C2×D191)⋊C8 | C22 | semidirect |
| 134. C191 | #3096 | semidirect |
| 145. C2×#102 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133230 | 2 |
| #27133144 | 2 |
| #27132986 | 2 |
| #27132985 | 2 |
| #27132980 | 2 |
| #27132975 | 2 |
| #27132703 | 2 |
| #27132701 | 2 |
| #27132668 | 2 |
| #27132629 | 2 |
| C2×#102×C191 | 2 |
| #3096 | 191 |