Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 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. C2×#16811063 | C2 | semidirect |
| 2. C2×#16810899 | C2 | semidirect |
| 4. C2×#16810428 | C2 | semidirect |
| 5. C2×#16810406 | C2 | semidirect |
| 6. #20272825 | C2 | semidirect |
| 7. C2×C53×#359 | C2 | semidirect |
| 41. C2×Dic212 | D4 | semidirect |
| 59. #13133157 | D4 | semidirect |
| 80. #108×C53 | D4 | semidirect |
| 208. C2×#359 | D53 | semidirect |
| 242. C53 | #13308 | semidirect |
| 287. #108 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811063 | 2 |
| C2×#16810899 | 2 |
| #20284381 | 2 |
| C2×#16810428 | 2 |
| C2×#16810406 | 2 |
| #20272825 | 2 |
| C2×C53×#359 | 2 |
| #13308 | 53 |