Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
882 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×C83⋊#564 | C2 | semidirect |
| 3. #24906764 | C2 | direct (N × H) |
| 4. C2×#19127443 | C2 | semidirect |
| 5. C2×#19127442 | C2 | semidirect |
| 9. C83⋊#564 | C22 | semidirect |
| 19. #19127443 | C22 | semidirect |
| 20. #19127442 | C22 | semidirect |
| 137. C2×C83 | #1658 | semidirect |
| 146. C83 | C2×#1658 | semidirect |
| 276. C2 | #24906764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C83⋊#564 | 2 |
| C2×#19128065 | 2 |
| #24906764 | 2 |
| C2×#19127443 | 2 |
| C2×#19127442 | 2 |
| C2×#490×C83 | 2 |
| C2×#1658 | 83 |