Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
682 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 187 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. #24909568 | C2 | direct (N × H) |
| 4. C2×#19127529 | C2 | semidirect |
| 5. C2×#19127505 | C2 | semidirect |
| 6. C22×Q32×C83 | C2 | semidirect |
| 16. #19127529 | C22 | semidirect |
| 17. #19127505 | C22 | semidirect |
| 20. C2×Q32×C83 | C22 | semidirect |
| 116. C2×C83 | #2219 | semidirect |
| 120. C22×Q32 | D83 | semidirect |
| 126. C83 | C2×#2219 | semidirect |
| 131. C2×Q32 | C2×D83 | semidirect |
| 236. C2 | #24909568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581731 | 2 |
| C2×#19127939 | 2 |
| #24909568 | 2 |
| C2×#19127529 | 2 |
| C2×#19127505 | 2 |
| C22×Q32×C83 | 2 |
| C2×#2219 | 83 |