Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1158 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 172 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. #20289553 | C2 | semidirect |
| 39. C23×C4×C53 | C8 | semidirect |
| 215. C53 | #8698 | semidirect |
| 235. C23×C4 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290537 | 2 |
| #20289553 | 2 |
| C22×#13133124 | 2 |
| #8698 | 53 |