Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
794 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#19127893 | C2 | semidirect |
| 2. #24908257 | C2 | semidirect |
| 3. C2×#19127445 | C2 | semidirect |
| 4. #24905298 | C2 | semidirect |
| 5. C2×#493×C83 | C2 | semidirect |
| 52. C2×D332 | D8 | semidirect |
| 86. C2×C8×C83 | D8 | semidirect |
| 159. C2×#493 | D83 | semidirect |
| 164. C83 | #10260 | semidirect |
| 243. C2×C8 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127893 | 2 |
| #24908257 | 2 |
| C2×#19127445 | 2 |
| #24905298 | 2 |
| C2×#493×C83 | 2 |
| #10260 | 83 |