Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 120 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. #20289734 | C2 | direct (N × H) |
| 117. C2×C53 | #1365 | semidirect |
| 136. C53 | C2×#1365 | semidirect |
| 229. C2 | #20289734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811544 | 2 |
| C2×#16811487 | 2 |
| #20289734 | 2 |
| C2×#16811027 | 2 |
| C2×#1365 | 53 |