Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
178 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 5. #16811555 | C4 | semidirect |
| 9. C2×#13133267 | C4 | semidirect |
| 90. C53 | #7470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811555 | 2 |
| C22×#13133267 | 2 |
| #20276312 | 2 |
| #7470 | 53 |