Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 102 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. #20290655 | C2 | semidirect |
| 4. #20289776 | C2 | semidirect |
| 162. Dic53 | #359 | semidirect |
| 194. C53 | #12815 | 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×#16811538 | 2 |
| #20290655 | 2 |
| #20289776 | 2 |
| C4×#13133240 | 2 |
| #12815 | 53 |