Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
698 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 129 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×D848 | C2 | semidirect |
| 2. C2×#16811000 | C2 | semidirect |
| 3. C2×#16810425 | C2 | semidirect |
| 4. #20275581 | C2 | semidirect |
| 5. C53×#1374 | C2 | semidirect |
| 35. C2×D424 | D4 | semidirect |
| 48. C2×C16×C53 | D4 | semidirect |
| 103. C2×C4×C53 | D16 | semidirect |
| 150. #1374 | D53 | semidirect |
| 172. C53 | #13325 | semidirect |
| 199. C2×C16 | D212 | semidirect |
| 267. C2×C4 | D848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16811000 | 2 |
| C2×#16810425 | 2 |
| #20275581 | 2 |
| C53×#1374 | 2 |
| #13325 | 53 |