Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27133208 | C2 | semidirect |
| 2. C2×#20259318 | C2 | semidirect |
| 3. #27133038 | C2 | semidirect |
| 4. #27133008 | C2 | semidirect |
| 5. #27132857 | C2 | semidirect |
| 6. #27132856 | C2 | semidirect |
| 7. #27132799 | C2 | semidirect |
| 8. #27132797 | C2 | semidirect |
| 9. #27132796 | C2 | semidirect |
| 10. #27132713 | C2 | semidirect |
| 11. #447×C191 | C2 | semidirect |
| 16. C2×D1528 | C22 | semidirect |
| 17. C2×#15690272 | C22 | semidirect |
| 18. C2×#15690272 | C22 | semidirect |
| 19. #20259321 | C22 | semidirect |
| 24. #20259318 | C22 | semidirect |
| 28. D4×Dic191 | C22 | semidirect |
| 29. #20259284 | C22 | semidirect |
| 32. Dic191⋊C8 | C22 | semidirect |
| 33. #20259244 | C22 | semidirect |
| 34. #20259243 | C22 | semidirect |
| 35. #20259242 | C22 | semidirect |
| 37. C8×Dic191 | C22 | semidirect |
| 39. C2×D8×C191 | C22 | semidirect |
| 41. #102×C191 | C22 | semidirect |
| 107. C2×Dic191 | D8 | semidirect |
| 164. C191 | #3205 | semidirect |
| 175. #447 | D191 | semidirect |
| 185. C2×D8 | C2×D191 | semidirect |
| 204. #102 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133208 | 2 |
| C2×#20259318 | 2 |
| #27133038 | 2 |
| #27133008 | 2 |
| #27132857 | 2 |
| #27132856 | 2 |
| #27132799 | 2 |
| #27132797 | 2 |
| #27132796 | 2 |
| #27132713 | 2 |
| #447×C191 | 2 |
| #3205 | 191 |