Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20277780 | C2 | semidirect |
| 2. #20275643 | C2 | semidirect |
| 3. C2×#16810367 | C2 | semidirect |
| 4. #20272555 | C2 | semidirect |
| 18. C53×#493 | C4 | semidirect |
| 46. #127×C53 | C2×C4 | semidirect |
| 50. C4×C8×C53 | C2×C4 | semidirect |
| 91. C4⋊Dic53 | D8 | semidirect |
| 180. #493 | Dic53 | semidirect |
| 189. C53 | #9061 | semidirect |
| 204. #127 | C2×Dic53 | semidirect |
| 219. C4×C8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277780 | 2 |
| #20275643 | 2 |
| C2×#16810367 | 2 |
| #20272555 | 2 |
| C2×C53×#493 | 2 |
| #9061 | 53 |