Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
698 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×#13133158 | C2 | semidirect |
| 3. C2×#16810998 | C2 | semidirect |
| 4. C2×#16810423 | C2 | semidirect |
| 5. #20275579 | C2 | semidirect |
| 6. #20272792 | C2 | semidirect |
| 7. C2×C53×#357 | C2 | semidirect |
| 43. C2×D424 | D4 | semidirect |
| 56. C2×#11719908 | D4 | semidirect |
| 71. C2×C16×C53 | D4 | semidirect |
| 161. C2×Dic53 | D16 | semidirect |
| 206. C2×#357 | D53 | semidirect |
| 238. C53 | #13325 | semidirect |
| 278. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C22×#13133158 | 2 |
| C2×#16810998 | 2 |
| C2×#16810423 | 2 |
| #20275579 | 2 |
| #20272792 | 2 |
| C2×C53×#357 | 2 |
| #13325 | 53 |