Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 108 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⋊(C4⋊C16) | C2 | semidirect |
| 3. #20290652 | C2 | semidirect |
| 4. #20289772 | C2 | semidirect |
| 15. C4×D424 | C4 | semidirect |
| 16. D8×Dic53 | C4 | semidirect |
| 17. #16810705 | C4 | semidirect |
| 23. C4×D8×C53 | C4 | semidirect |
| 198. C4×D8 | #6157 | semidirect |
| 208. C53 | #12813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C4⋊C16) | 2 |
| C2×#16811535 | 2 |
| #20290652 | 2 |
| #20289772 | 2 |
| C4×D8×D53 | 2 |
| #12813 | 53 |