Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 23. #16810428 | C4 | semidirect |
| 24. #16810427 | C4 | semidirect |
| 25. #16810426 | C4 | semidirect |
| 26. C53×#358 | C4 | semidirect |
| 182. #358 | #6157 | semidirect |
| 184. C53 | #12957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811663 | 2 |
| C2×#16811547 | 2 |
| C2×#16811542 | 2 |
| #20290824 | 2 |
| #20289786 | 2 |
| #20289755 | 2 |
| #20276433 | 2 |
| #12957 | 53 |