Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #24909714 | C2 | semidirect |
| 5. Dic83⋊C32 | C2 | semidirect |
| 6. #24905643 | C2 | semidirect |
| 7. C83×#1416 | C2 | semidirect |
| 89. Dic83 | SD64 | semidirect |
| 101. #1416 | D83 | semidirect |
| 102. C83 | #13687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127540 | 2 |
| C2×#19127538 | 2 |
| #24909714 | 2 |
| #24909309 | 2 |
| Dic83⋊C32 | 2 |
| #24905643 | 2 |
| C83×#1416 | 2 |
| #13687 | 83 |