Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 78 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. D53⋊M64 | C2 | semidirect |
| 2. #20291066 | C2 | semidirect |
| 3. #20289864 | C2 | semidirect |
| 8. D53⋊C32 | C22 | semidirect |
| 10. #16811549 | C22 | semidirect |
| 12. C2×D848 | C4 | semidirect |
| 16. D16×D53 | C4 | semidirect |
| 19. C2×D16×C53 | C4 | semidirect |
| 129. C2×D16 | #6157 | semidirect |
| 137. C53 | #13617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| #20291066 | 2 |
| #20289864 | 2 |
| C2×D16×D53 | 2 |
| #13617 | 53 |