Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
| 2. D53⋊#334 | C2 | semidirect |
| 3. #20289728 | C2 | semidirect |
| 4. #20289727 | C2 | semidirect |
| 8. #16811544 | C22 | semidirect |
| 10. #16811485 | C22 | semidirect |
| 174. D53 | #1360 | semidirect |
| 192. C53 | C2×#1360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C4⋊C16) | 2 |
| D53⋊#334 | 2 |
| #20289728 | 2 |
| #20289727 | 2 |
| #495×D53 | 2 |
| C2×#1360 | 53 |