Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
546 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#16811001 | C2 | semidirect |
| 4. C2×#16810438 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C2×C53×#362 | C2 | semidirect |
| 193. C2×#362 | D53 | semidirect |
| 224. C53 | #13333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811066 | 2 |
| C2×#16811064 | 2 |
| C2×#16811001 | 2 |
| C2×#16810438 | 2 |
| #20275601 | 2 |
| #20272796 | 2 |
| C2×C53×#362 | 2 |
| #13333 | 53 |