Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
370 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20289794 | C2 | semidirect |
| 4. #20289784 | C2 | semidirect |
| 170. C53 | #12876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#349 | 2 |
| #20290596 | 2 |
| #20289794 | 2 |
| #20289784 | 2 |
| #430×D53 | 2 |
| #12876 | 53 |