Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
556 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 1. C22×#13133158 | C2 | semidirect |
| 2. C2×#16810894 | C2 | semidirect |
| 3. C2×#16810890 | C2 | semidirect |
| 4. C2×#16810437 | C2 | semidirect |
| 5. #20276330 | C2 | semidirect |
| 6. #20272808 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 195. C2×#361 | D53 | semidirect |
| 226. C53 | #13313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133158 | 2 |
| C2×#16810894 | 2 |
| C2×#16810890 | 2 |
| C2×#16810437 | 2 |
| #20276330 | 2 |
| #20272808 | 2 |
| C2×C53×#361 | 2 |
| #13313 | 53 |