Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 14. #16811547 | C4 | semidirect |
| 15. #16811513 | C4 | semidirect |
| 21. #16810451 | C4 | semidirect |
| 22. #16810450 | C4 | semidirect |
| 23. #16810448 | C4 | semidirect |
| 24. C53×#366 | C4 | semidirect |
| 84. C16×C53 | C42 | semidirect |
| 85. #11719908 | C42 | semidirect |
| 151. #366 | #6157 | semidirect |
| 156. C53 | #12677 | semidirect |
| 217. C16 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811547 | 2 |
| C2×#16811513 | 2 |
| #20290530 | 2 |
| #20290522 | 2 |
| #20289789 | 2 |
| #20289786 | 2 |
| #20276500 | 2 |
| #12677 | 53 |