Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 1. #27133194 | C2 | semidirect |
| 2. C2×#20259311 | C2 | semidirect |
| 3. #27133044 | C2 | semidirect |
| 4. #27133019 | C2 | semidirect |
| 5. #27132888 | C2 | semidirect |
| 6. #27132880 | C2 | semidirect |
| 7. #27132819 | C2 | semidirect |
| 8. #27132816 | C2 | semidirect |
| 10. #27132713 | C2 | semidirect |
| 11. #448×C191 | C2 | semidirect |
| 13. C2×#15690277 | C22 | semidirect |
| 17. #20259313 | C22 | semidirect |
| 22. #20259309 | C22 | semidirect |
| 25. #20259287 | C22 | semidirect |
| 27. D4×Dic191 | C22 | semidirect |
| 32. Dic191⋊C8 | C22 | semidirect |
| 33. #20259246 | C22 | semidirect |
| 37. C8×Dic191 | C22 | semidirect |
| 39. C2×SD16×C191 | C22 | semidirect |
| 41. #103×C191 | C22 | semidirect |
| 143. C191 | #3211 | semidirect |
| 153. #448 | D191 | semidirect |
| 160. C2×SD16 | C2×D191 | semidirect |
| 181. #103 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133194 | 2 |
| C2×#20259311 | 2 |
| #27133044 | 2 |
| #27133019 | 2 |
| #27132888 | 2 |
| #27132880 | 2 |
| #27132819 | 2 |
| #27132816 | 2 |
| #27132796 | 2 |
| #27132713 | 2 |
| #448×C191 | 2 |
| #3211 | 191 |