Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 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. #20290916 | C2 | semidirect |
| 2. D53⋊#334 | C2 | semidirect |
| 3. #20289674 | C2 | semidirect |
| 4. #20289673 | C2 | semidirect |
| 8. #16811512 | C22 | semidirect |
| 11. #16811484 | C22 | semidirect |
| 33. D8×D53 | C8 | semidirect |
| 75. D8×C53 | C2×C8 | semidirect |
| 93. D424 | C2×C8 | semidirect |
| 163. D53 | #1333 | semidirect |
| 181. C53 | C2×#1333 | semidirect |
| 235. D8 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290916 | 2 |
| D53⋊#334 | 2 |
| #20289674 | 2 |
| #20289673 | 2 |
| C4×D8×D53 | 2 |
| C2×#1333 | 53 |