Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 189. C53 | #9788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811022 | 2 |
| #20273476 | 2 |
| #20273316 | 2 |
| #20273072 | 2 |
| #20273071 | 2 |
| M16×#88322 | 2 |
| C53×#1528 | 2 |
| #9788 | 53 |