Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 9. #16811489 | C4 | semidirect |
| 12. C2×C4×#88322 | C4 | semidirect |
| 14. C2×C4×C8×C53 | C4 | semidirect |
| 26. (C2×#6157)⋊C4 | C8 | semidirect |
| 179. C2×C4×C8 | #6157 | semidirect |
| 185. C53 | #7024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290572 | 2 |
| #20289891 | 2 |
| C4×#13133129 | 2 |
| #7024 | 53 |