Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #20272875 | C2 | direct (N × H) |
| 13. C2×C4⋊Q8×C53 | C4 | semidirect |
| 17. C53×#497 | C4 | semidirect |
| 19. C2×#97×C53 | C4 | semidirect |
| 40. C4⋊Q8×C53 | C2×C4 | semidirect |
| 50. #97×C53 | C2×C4 | semidirect |
| 155. C2×C53 | #1407 | semidirect |
| 159. C2×C4⋊Q8 | Dic53 | semidirect |
| 163. #497 | Dic53 | semidirect |
| 167. C2×#97 | Dic53 | semidirect |
| 172. C53 | C2×#1407 | semidirect |
| 188. C4⋊Q8 | C2×Dic53 | semidirect |
| 203. #97 | C2×Dic53 | semidirect |
| 303. C2 | #20272875 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810420 | 2 |
| C2×#16810418 | 2 |
| #20272875 | 2 |
| C2×C53×#497 | 2 |
| C2×#1407 | 53 |