Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
248 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 3. #20289634 | C2 | semidirect |
| 4. #20289631 | C2 | semidirect |
| 59. C16×C53 | M16 | semidirect |
| 61. #11719908 | M16 | semidirect |
| 115. C53 | #11414 | semidirect |
| 157. C16 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291079 | 2 |
| #20289925 | 2 |
| #20289634 | 2 |
| #20289631 | 2 |
| C4×#13133156 | 2 |
| #11414 | 53 |