Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
178 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 6. #16811556 | C4 | semidirect |
| 9. #16811550 | C4 | semidirect |
| 13. #16810449 | C4 | semidirect |
| 14. C53×#366 | C4 | semidirect |
| 95. #366 | #6157 | semidirect |
| 96. C53 | #7477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811556 | 2 |
| C2×#16811550 | 2 |
| #20276496 | 2 |
| #7477 | 53 |