Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1294 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1294 conjugacy classes of subgroups — too many to draw. Only its 228 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. C2×#16811499 | C2 | semidirect |
| 174. C53 | #10724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811594 | 2 |
| C2×#16811499 | 2 |
| C22×M16×D53 | 2 |
| #10724 | 53 |