Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C2×#16811548 | C2 | semidirect |
| 4. #20290832 | C2 | semidirect |
| 5. #20289784 | C2 | semidirect |
| 6. #20289764 | C2 | semidirect |
| 25. #16810431 | C4 | semidirect |
| 26. #16810430 | C4 | semidirect |
| 27. #16810429 | C4 | semidirect |
| 28. C53×#359 | C4 | semidirect |
| 202. #359 | #6157 | semidirect |
| 204. C53 | #12948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291494 | 2 |
| C2×#16811548 | 2 |
| D53⋊#360 | 2 |
| #20290832 | 2 |
| #20289784 | 2 |
| #20289764 | 2 |
| #20276441 | 2 |
| #12948 | 53 |