Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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. #24918034 | C2 | semidirect |
| 2. #24909629 | C2 | semidirect |
| 3. #24909623 | C2 | semidirect |
| 4. #24909561 | C2 | semidirect |
| 6. #24909527 | C2 | semidirect |
| 7. #24909521 | C2 | semidirect |
| 8. C2×Dic83⋊C16 | C2 | semidirect |
| 9. C83×#2216 | C2 | semidirect |
| 151. #2216 | D83 | semidirect |
| 156. C83 | #33816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918034 | 2 |
| #24909629 | 2 |
| #24909623 | 2 |
| #24909561 | 2 |
| #24909549 | 2 |
| #24909527 | 2 |
| #24909521 | 2 |
| C2×Dic83⋊C16 | 2 |
| C83×#2216 | 2 |
| #33816 | 83 |