Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24916504 | C2 | semidirect |
| 3. #24906022 | C2 | semidirect |
| 4. #24905861 | C2 | semidirect |
| 5. #24905360 | C2 | semidirect |
| 6. #24905321 | C2 | semidirect |
| 7. C83×#1804 | C2 | semidirect |
| 11. #19127906 | C4 | semidirect |
| 12. #19127896 | C4 | semidirect |
| 197. #1804 | D83 | semidirect |
| 202. C83 | #9309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916927 | 2 |
| #24916504 | 2 |
| #24906022 | 2 |
| #24905861 | 2 |
| #24905360 | 2 |
| #24905321 | 2 |
| C83×#1804 | 2 |
| #9309 | 83 |