Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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×#19129195 | C2 | semidirect |
| 2. D337⋊M16 | C2 | direct (N × H) |
| 3. C2×#19129194 | C2 | semidirect |
| 4. C2×#19129193 | C2 | semidirect |
| 6. #19129195 | C22 | semidirect |
| 7. #19129194 | C22 | semidirect |
| 8. #19129193 | C22 | semidirect |
| 9. C2×#14582113 | C22 | semidirect |
| 19. #14582113 | C23 | semidirect |
| 43. C2×D337 | M16 | semidirect |
| 52. C2×C337 | C2×M16 | semidirect |
| 55. D337 | C2×M16 | semidirect |
| 56. C337 | C22×M16 | semidirect |
| 111. C2 | D337⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19129195 | 2 |
| D337⋊M16 | 2 |
| C2×#19129194 | 2 |
| C2×#19129193 | 2 |
| C22×C4×D337 | 2 |
| C22×M16 | 337 |