Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. C2×#19127443 | C2 | semidirect |
| 5. #24905361 | C2 | semidirect |
| 6. #24905307 | C2 | semidirect |
| 7. C83×#1470 | C2 | semidirect |
| 198. #1470 | D83 | semidirect |
| 201. C83 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918631 | 2 |
| #24916452 | 2 |
| #24906084 | 2 |
| C2×#19127443 | 2 |
| #24905361 | 2 |
| #24905307 | 2 |
| C83×#1470 | 2 |
| #9266 | 83 |