Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16810860 | C2 | semidirect |
| 3. C2×#16810423 | C2 | semidirect |
| 4. C2×#16810402 | C2 | semidirect |
| 5. C53×#1380 | C2 | semidirect |
| 27. C2×D424 | D4 | semidirect |
| 43. C2×C16×C53 | D4 | semidirect |
| 45. #107×C53 | D4 | semidirect |
| 94. C22×D53 | D16 | semidirect |
| 143. #1380 | D53 | semidirect |
| 164. C53 | #13304 | semidirect |
| 188. C2×C16 | D212 | semidirect |
| 190. #107 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810860 | 2 |
| C2×#16810423 | 2 |
| C2×#16810402 | 2 |
| C53×#1380 | 2 |
| #13304 | 53 |