Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20291079 | C2 | semidirect |
| 2. #20290270 | C2 | semidirect |
| 3. #20289674 | C2 | semidirect |
| 4. #20289673 | C2 | semidirect |
| 9. #16811512 | C22 | semidirect |
| 11. #16811484 | C22 | semidirect |
| 74. D8×C53 | M16 | semidirect |
| 92. D424 | M16 | semidirect |
| 180. C53 | #11663 | semidirect |
| 233. D8 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291079 | 2 |
| #20290270 | 2 |
| #20289674 | 2 |
| #20289673 | 2 |
| C4×D8×D53 | 2 |
| #11663 | 53 |