Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24907273 | C2 | semidirect |
| 3. #24906054 | C2 | semidirect |
| 4. #24905972 | C2 | semidirect |
| 5. #24905357 | C2 | semidirect |
| 6. #24905336 | C2 | semidirect |
| 7. C83×#2971 | C2 | semidirect |
| 10. #19127986 | C4 | semidirect |
| 11. #19127981 | C4 | semidirect |
| 12. #19127901 | C4 | semidirect |
| 13. #19127896 | C4 | semidirect |
| 204. #2971 | D83 | semidirect |
| 210. C83 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917614 | 2 |
| #24907273 | 2 |
| #24906054 | 2 |
| #24905972 | 2 |
| #24905357 | 2 |
| #24905336 | 2 |
| C83×#2971 | 2 |
| #9162 | 83 |