Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#19128141 | C2 | semidirect |
| 2. C22×#14581737 | C2 | semidirect |
| 4. #24916330 | C2 | semidirect |
| 5. #24909528 | C2 | semidirect |
| 6. #24909502 | C2 | semidirect |
| 7. #24909221 | C2 | semidirect |
| 8. #24909178 | C2 | semidirect |
| 9. C83×#2138 | C2 | semidirect |
| 16. C2×#14581738 | C22 | semidirect |
| 19. C2×#14581736 | C22 | semidirect |
| 25. #19127795 | C22 | semidirect |
| 28. Dic83⋊C16 | C22 | semidirect |
| 33. #358×C83 | C22 | semidirect |
| 34. #357×C83 | C22 | semidirect |
| 40. C2×Dic332 | D4 | semidirect |
| 185. #2138 | D83 | semidirect |
| 186. C83 | #33587 | semidirect |
| 209. #358 | C2×D83 | semidirect |
| 211. #357 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128141 | 2 |
| C22×#14581737 | 2 |
| #24917950 | 2 |
| #24916330 | 2 |
| #24909528 | 2 |
| #24909502 | 2 |
| #24909221 | 2 |
| #24909178 | 2 |
| C83×#2138 | 2 |
| #33587 | 83 |