Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27133029 | C2 | semidirect |
| 3. #27133025 | C2 | semidirect |
| 4. #27133020 | C2 | semidirect |
| 5. #27133011 | C2 | semidirect |
| 6. #27132667 | C2 | semidirect |
| 7. #27132662 | C2 | semidirect |
| 8. #27132657 | C2 | semidirect |
| 9. C2×#20259242 | C2 | semidirect |
| 10. #27132619 | C2 | semidirect |
| 11. #544×C191 | C2 | semidirect |
| 21. #20259245 | C22 | semidirect |
| 22. #20259245 | C22 | semidirect |
| 23. #20259245 | C22 | semidirect |
| 28. #20259242 | C22 | semidirect |
| 29. #20259242 | C22 | semidirect |
| 30. #20259242 | C22 | semidirect |
| 31. #20259233 | C22 | semidirect |
| 32. C4×C191⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C191 | C22 | semidirect |
| 36. #125×C191 | C22 | semidirect |
| 135. C191 | #3136 | semidirect |
| 137. #544 | D191 | semidirect |
| 153. C4⋊Q8 | C2×D191 | semidirect |
| 156. #125 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133232 | 2 |
| #27133029 | 2 |
| #27133025 | 2 |
| #27133020 | 2 |
| #27133011 | 2 |
| #27132667 | 2 |
| #27132662 | 2 |
| #27132657 | 2 |
| C2×#20259242 | 2 |
| #27132619 | 2 |
| #544×C191 | 2 |
| #3136 | 191 |