Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20289754 | C2 | semidirect |
| 2. #20289545 | C2 | semidirect |
| 30. C2×D8×C53 | C8 | semidirect |
| 138. C53 | #7112 | semidirect |
| 143. C2×D8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289754 | 2 |
| #20289545 | 2 |
| #20275582 | 2 |
| #7112 | 53 |