Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 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×#19128136 | C2 | semidirect |
| 2. C22×D1328 | C2 | semidirect |
| 3. #24917950 | C2 | semidirect |
| 4. #24916314 | C2 | semidirect |
| 5. #24909521 | C2 | semidirect |
| 6. #24909497 | C2 | semidirect |
| 7. #24909221 | C2 | semidirect |
| 8. #24909178 | C2 | semidirect |
| 9. C83×#2138 | C2 | semidirect |
| 16. C2×#14581735 | C22 | semidirect |
| 19. C2×#14581733 | C22 | semidirect |
| 22. #19128086 | C22 | semidirect |
| 23. #19128076 | C22 | semidirect |
| 25. #19127783 | C22 | semidirect |
| 28. Dic83⋊C16 | C22 | semidirect |
| 29. #19127501 | C22 | semidirect |
| 33. #358×C83 | C22 | semidirect |
| 34. #357×C83 | C22 | semidirect |
| 44. C2×D664 | D4 | semidirect |
| 190. #2138 | D83 | semidirect |
| 191. C83 | #33585 | semidirect |
| 214. #358 | C2×D83 | semidirect |
| 216. #357 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128136 | 2 |
| C22×D1328 | 2 |
| #24917950 | 2 |
| #24916314 | 2 |
| #24909521 | 2 |
| #24909497 | 2 |
| #24909221 | 2 |
| #24909178 | 2 |
| C83×#2138 | 2 |
| #33585 | 83 |