Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
734 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16810347 | C2 | semidirect |
| 2. #20272645 | C2 | semidirect |
| 3. #20272643 | C2 | semidirect |
| 27. C22×D4×C53 | C8 | semidirect |
| 54. C24×C53 | C2×C8 | semidirect |
| 77. C22×C4×C53 | C2×C8 | semidirect |
| 199. C53 | #11426 | semidirect |
| 207. C22×D4 | #88322 | semidirect |
| 235. C24 | C2×#88322 | semidirect |
| 259. C22×C4 | C2×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810347 | 2 |
| #20272645 | 2 |
| #20272643 | 2 |
| C53×#2308 | 2 |
| #11426 | 53 |