Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 2. #20289746 | C2 | semidirect |
| 40. C16×C53 | M16 | semidirect |
| 87. C53 | #12022 | semidirect |
| 117. C16 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290273 | 2 |
| #20289746 | 2 |
| C4×C16×D53 | 2 |
| #12022 | 53 |