Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 3. #20275536 | C2 | semidirect |
| 4. C2×#16810365 | C2 | semidirect |
| 6. #20272597 | C2 | semidirect |
| 7. C2×C53×#501 | C2 | semidirect |
| 186. C2×#501 | D53 | semidirect |
| 222. C53 | #10086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810985 | 2 |
| #20282765 | 2 |
| #20275536 | 2 |
| C2×#16810365 | 2 |
| C2×#16810362 | 2 |
| #20272597 | 2 |
| C2×C53×#501 | 2 |
| #10086 | 53 |