Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #20274711 | C2 | semidirect |
| 4. #20272841 | C2 | semidirect |
| 5. C53×#1801 | C2 | semidirect |
| 189. C4×C53 | #355 | semidirect |
| 196. #1801 | D53 | semidirect |
| 222. C53 | #12801 | semidirect |
| 390. C4 | #16810419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133206 | 2 |
| C2×#16810419 | 2 |
| #20274711 | 2 |
| #20272841 | 2 |
| C53×#1801 | 2 |
| #12801 | 53 |