Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#20259298 | C2 | semidirect |
| 3. #27133003 | C2 | semidirect |
| 4. #27132999 | C2 | semidirect |
| 5. #27132979 | C2 | semidirect |
| 6. #27132920 | C2 | semidirect |
| 7. #27132906 | C2 | semidirect |
| 8. #27132822 | C2 | semidirect |
| 9. #27132819 | C2 | semidirect |
| 10. #27132625 | C2 | semidirect |
| 11. #448×C191 | C2 | semidirect |
| 14. C2×#15690277 | C22 | semidirect |
| 31. #20259256 | C22 | semidirect |
| 32. #20259253 | C22 | semidirect |
| 33. #20259247 | C22 | semidirect |
| 34. #20259246 | C22 | semidirect |
| 35. #20259243 | C22 | semidirect |
| 39. C2×SD16×C191 | C22 | semidirect |
| 41. #103×C191 | C22 | semidirect |
| 149. C191 | #3196 | semidirect |
| 160. #448 | D191 | semidirect |
| 166. C2×SD16 | C2×D191 | semidirect |
| 188. #103 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133173 | 2 |
| C2×#20259298 | 2 |
| #27133003 | 2 |
| #27132999 | 2 |
| #27132979 | 2 |
| #27132920 | 2 |
| #27132906 | 2 |
| #27132822 | 2 |
| #27132819 | 2 |
| #27132625 | 2 |
| #448×C191 | 2 |
| #3196 | 191 |