Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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. D337⋊M16 | C2 | semidirect |
| 2. #24925038 | C2 | semidirect |
| 3. #24925024 | C2 | semidirect |
| 5. #19129195 | C22 | semidirect |
| 10. C4×#13062438 | C22 | semidirect |
| 13. #19129186 | C4 | semidirect |
| 16. C2×D1348 | C4 | semidirect |
| 19. C2×Q8×C337 | C4 | semidirect |
| 56. C337 | #421 | semidirect |
| 66. C2×Q8 | #13062438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D337⋊M16 | 2 |
| #24925038 | 2 |
| #24925024 | 2 |
| C2×#19129186 | 2 |
| #421 | 337 |