Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
518 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 518 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 |
| 2. D53⋊#335 | C2 | semidirect |
| 3. #20289729 | C2 | semidirect |
| 7. #16811544 | C22 | semidirect |
| 9. #16811487 | C22 | semidirect |
| 152. D53 | #1361 | semidirect |
| 168. C53 | C2×#1361 | 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⋊#335 | 2 |
| #20289729 | 2 |
| #493×D53 | 2 |
| C2×#1361 | 53 |