Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
558 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#19127503 | C2 | semidirect |
| 3. #24907492 | C2 | semidirect |
| 4. #24905555 | C2 | semidirect |
| 5. C22×M32×C83 | C2 | semidirect |
| 9. #19127937 | C4 | semidirect |
| 48. C2×C16×C83 | D4 | semidirect |
| 146. C22×M32 | D83 | semidirect |
| 151. C83 | #13061 | semidirect |
| 188. C2×C16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127937 | 2 |
| C2×#19127503 | 2 |
| #24907492 | 2 |
| #24905555 | 2 |
| C22×M32×C83 | 2 |
| #13061 | 83 |