Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
958 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 958 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 |
|---|---|---|
| 1. C2×#19128071 | C2 | semidirect |
| 2. C2×#19128060 | C2 | semidirect |
| 3. #24906786 | C2 | direct (N × H) |
| 4. C2×#19127443 | C2 | semidirect |
| 5. C2×#19127441 | C2 | semidirect |
| 9. #19128071 | C22 | semidirect |
| 11. #19128060 | C22 | semidirect |
| 17. #19127443 | C22 | semidirect |
| 18. #19127441 | C22 | semidirect |
| 146. C2×C83 | #1662 | semidirect |
| 155. C83 | C2×#1662 | semidirect |
| 294. C2 | #24906786 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128071 | 2 |
| C2×#19128060 | 2 |
| #24906786 | 2 |
| C2×#19127443 | 2 |
| C2×#19127441 | 2 |
| C2×#562×C83 | 2 |
| C2×#1662 | 83 |