Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
470 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24916546 | C2 | semidirect |
| 3. #24907475 | C2 | semidirect |
| 6. #24905358 | C2 | semidirect |
| 7. C83×#1286 | C2 | semidirect |
| 12. #19127912 | C4 | semidirect |
| 13. #19127902 | C4 | semidirect |
| 190. #1286 | D83 | semidirect |
| 191. C83 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916937 | 2 |
| #24916546 | 2 |
| #24907475 | 2 |
| #24906022 | 2 |
| #24905863 | 2 |
| #24905358 | 2 |
| C83×#1286 | 2 |
| #9310 | 83 |