Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. #20274711 | C2 | semidirect |
| 3. #20273474 | C2 | semidirect |
| 6. #20272590 | C2 | semidirect |
| 7. C2×C53×Q8⋊C8 | C2 | semidirect |
| 188. C2×Q8⋊C8 | D53 | semidirect |
| 217. C53 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284187 | 2 |
| #20274711 | 2 |
| #20273474 | 2 |
| #20273390 | 2 |
| #20273167 | 2 |
| #20272590 | 2 |
| C2×C53×Q8⋊C8 | 2 |
| #10458 | 53 |