Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 10. #16811550 | C4 | semidirect |
| 11. C16×#6157 | C4 | semidirect |
| 15. #16810451 | C4 | semidirect |
| 16. #16810450 | C4 | semidirect |
| 17. C53×#367 | C4 | semidirect |
| 62. C16×C53 | C42 | semidirect |
| 63. #11719908 | C42 | semidirect |
| 95. #6157 | #367 | direct (N × H) |
| 121. #367 | #6157 | direct (N × H) |
| 124. C53 | C4×#367 | semidirect |
| 170. C16 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811550 | 2 |
| C2×C16×#6157 | 2 |
| #107×#6157 | 2 |
| #20289772 | 2 |
| #367×D53 | 2 |
| C4×#367 | 53 |