Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
572 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20272842 | C2 | semidirect |
| 3. C53×#2811 | C2 | semidirect |
| 13. #13133265 | Q8 | semidirect |
| 99. #2811 | D53 | semidirect |
| 115. C53 | #13378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274673 | 2 |
| #20272842 | 2 |
| C53×#2811 | 2 |
| #13378 | 53 |