Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
622 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #20272563 | C2 | semidirect |
| 27. C2×C22⋊C4×C53 | C8 | semidirect |
| 161. C53 | #8734 | semidirect |
| 173. C2×C22⋊C4 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810347 | 2 |
| #20272563 | 2 |
| C53×#2273 | 2 |
| #8734 | 53 |