Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 5. C2×#13133286 | C4 | semidirect |
| 7. #16811518 | C4 | semidirect |
| 12. #16810386 | C4 | semidirect |
| 14. C53×#340 | C4 | semidirect |
| 156. #340 | #6157 | semidirect |
| 157. C53 | #7258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290592 | 2 |
| #340×D53 | 2 |
| #7258 | 53 |