Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 112 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. #16811552 | C4 | semidirect |
| 11. C16×#6157 | C4 | semidirect |
| 15. #16810451 | C4 | semidirect |
| 16. #16810448 | C4 | semidirect |
| 17. C53×#367 | C4 | semidirect |
| 110. #367 | #6157 | semidirect |
| 114. C53 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811552 | 2 |
| C2×C16×#6157 | 2 |
| #20290519 | 2 |
| #20289776 | 2 |
| #20276498 | 2 |
| #12670 | 53 |