Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 8. #16810349 | C4 | semidirect |
| 11. C2×C4⋊C8×C53 | C4 | semidirect |
| 14. C2×C4×C8×C53 | C4 | semidirect |
| 19. #13133132 | C8 | semidirect |
| 151. C2×C4⋊C8 | Dic53 | semidirect |
| 156. C2×C4×C8 | Dic53 | semidirect |
| 161. C53 | #7205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133132 | 2 |
| #20273033 | 2 |
| C53×#1954 | 2 |
| #7205 | 53 |