Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
466 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 466 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. #27133176 | C2 | semidirect |
| 2. C2×#20259293 | C2 | semidirect |
| 3. #27132991 | C2 | semidirect |
| 4. #27132985 | C2 | semidirect |
| 5. #27132977 | C2 | semidirect |
| 6. #27132915 | C2 | semidirect |
| 7. #27132906 | C2 | semidirect |
| 8. #27132807 | C2 | semidirect |
| 9. #27132797 | C2 | semidirect |
| 10. #27132625 | C2 | semidirect |
| 11. #450×C191 | C2 | semidirect |
| 12. C2×#15690288 | C22 | semidirect |
| 15. C2×#15690272 | C22 | semidirect |
| 16. C2×#15690270 | C22 | semidirect |
| 18. #20259298 | C22 | semidirect |
| 19. #20259297 | C22 | semidirect |
| 28. #20259280 | C22 | semidirect |
| 31. #20259256 | C22 | semidirect |
| 32. #20259253 | C22 | semidirect |
| 33. #20259246 | C22 | semidirect |
| 34. #20259244 | C22 | semidirect |
| 35. #20259243 | C22 | semidirect |
| 37. (C2×D191)⋊C8 | C22 | semidirect |
| 39. C2×SD16×C191 | C22 | semidirect |
| 41. #102×C191 | C22 | semidirect |
| 158. C191 | #3194 | semidirect |
| 167. #450 | D191 | semidirect |
| 175. C2×SD16 | C2×D191 | semidirect |
| 198. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133176 | 2 |
| C2×#20259293 | 2 |
| #27132991 | 2 |
| #27132985 | 2 |
| #27132977 | 2 |
| #27132915 | 2 |
| #27132906 | 2 |
| #27132807 | 2 |
| #27132797 | 2 |
| #27132625 | 2 |
| #450×C191 | 2 |
| #3194 | 191 |