Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
736 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 140 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. #20289807 | C2 | semidirect |
| 3. #20289806 | C2 | semidirect |
| 220. C53 | #12579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#413 | 2 |
| #20289807 | 2 |
| #20289806 | 2 |
| #20283157 | 2 |
| #12579 | 53 |