Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
768 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20285466 | C2 | semidirect |
| 2. #20283967 | C2 | semidirect |
| 3. #20273074 | C2 | semidirect |
| 4. #20272592 | C2 | semidirect |
| 5. C53×#1780 | C2 | semidirect |
| 162. #1780 | D53 | semidirect |
| 187. C53 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285466 | 2 |
| #20283967 | 2 |
| #20273074 | 2 |
| #20272592 | 2 |
| C53×#1780 | 2 |
| #9974 | 53 |