Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
906 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 1. #20285294 | C2 | semidirect |
| 2. #20285143 | C2 | semidirect |
| 3. #20274386 | C2 | semidirect |
| 4. #20274381 | C2 | semidirect |
| 5. C2×C53×#322 | C2 | semidirect |
| 49. C2×C8×C53 | D8 | semidirect |
| 92. C2×#322 | D53 | semidirect |
| 111. C53 | #19616 | semidirect |
| 145. C2×C8 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| #20285143 | 2 |
| #20274386 | 2 |
| #20274381 | 2 |
| C2×C53×#322 | 2 |
| #19616 | 53 |