Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 67 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. Q32×Dic83 | C2 | semidirect |
| 4. #24905664 | C2 | semidirect |
| 6. C32×Dic83 | C2 | semidirect |
| 7. C83×#1416 | C2 | semidirect |
| 11. #19127538 | C4 | semidirect |
| 30. C83⋊C32 | C2×C4 | semidirect |
| 33. Q32×C83 | C2×C4 | semidirect |
| 80. Dic83 | SD64 | semidirect |
| 90. #1416 | D83 | semidirect |
| 93. C83 | C4×SD64 | semidirect |
| 111. Q32 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127538 | 2 |
| Q32×Dic83 | 2 |
| #24909309 | 2 |
| #24905664 | 2 |
| #24905642 | 2 |
| C32×Dic83 | 2 |
| C83×#1416 | 2 |
| C4×SD64 | 83 |