Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
516 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 1. C22×#14581738 | C2 | semidirect |
| 4. C2×#19127518 | C2 | semidirect |
| 6. #24905556 | C2 | semidirect |
| 7. C2×#362×C83 | C2 | semidirect |
| 192. C2×#362 | D83 | semidirect |
| 195. C83 | #13315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581738 | 2 |
| C2×#19127977 | 2 |
| C2×#19127973 | 2 |
| C2×#19127518 | 2 |
| #24909078 | 2 |
| #24905556 | 2 |
| C2×#362×C83 | 2 |
| #13315 | 83 |