Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 45 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. #20272655 | C2 | semidirect |
| 3. C53×#1290 | C2 | semidirect |
| 99. #1290 | D53 | semidirect |
| 113. C53 | #7080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276026 | 2 |
| #20272655 | 2 |
| C53×#1290 | 2 |
| #7080 | 53 |