Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20273474 | C2 | semidirect |
| 3. #20272769 | C2 | semidirect |
| 4. #20272762 | C2 | semidirect |
| 5. C2×C53×C4⋊C16 | C2 | semidirect |
| 126. C2×C4⋊C16 | D53 | semidirect |
| 150. C53 | #11981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| #20273474 | 2 |
| #20272769 | 2 |
| #20272762 | 2 |
| C2×C53×C4⋊C16 | 2 |
| #11981 | 53 |