Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4×#14581725 | C2 | semidirect |
| 3. #24906224 | C2 | semidirect |
| 6. #24905320 | C2 | semidirect |
| 7. C83×#1285 | C2 | semidirect |
| 9. #19127828 | C4 | semidirect |
| 10. #19127825 | C4 | semidirect |
| 11. #19127778 | C4 | semidirect |
| 13. #19127766 | C4 | semidirect |
| 185. #1285 | D83 | semidirect |
| 186. C83 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916432 | 2 |
| C4×#14581725 | 2 |
| #24906224 | 2 |
| #24905989 | 2 |
| #24905986 | 2 |
| #24905320 | 2 |
| C83×#1285 | 2 |
| #8697 | 83 |