Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
716 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. C22×#14581735 | C2 | semidirect |
| 3. #24917952 | C2 | semidirect |
| 4. #24916314 | C2 | semidirect |
| 5. #24909521 | C2 | semidirect |
| 6. #24909507 | C2 | semidirect |
| 7. #24909223 | C2 | semidirect |
| 8. #24909168 | C2 | semidirect |
| 9. C83×#2141 | C2 | semidirect |
| 22. #19128086 | C22 | semidirect |
| 23. #19128079 | C22 | semidirect |
| 28. Dic83⋊C16 | C22 | semidirect |
| 29. #19127504 | C22 | semidirect |
| 30. #19127501 | C22 | semidirect |
| 34. #358×C83 | C22 | semidirect |
| 184. #2141 | D83 | semidirect |
| 186. C83 | #33586 | semidirect |
| 210. #358 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128139 | 2 |
| C22×#14581735 | 2 |
| #24917952 | 2 |
| #24916314 | 2 |
| #24909521 | 2 |
| #24909507 | 2 |
| #24909223 | 2 |
| #24909168 | 2 |
| C83×#2141 | 2 |
| #33586 | 83 |