Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
180 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 15. #125×C53 | C8 | semidirect |
| 76. C53 | #7358 | semidirect |
| 80. #125 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289657 | 2 |
| #20275685 | 2 |
| #7358 | 53 |