Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20273352 | C2 | semidirect |
| 5. #20273117 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 7. C53×#1290 | C2 | semidirect |
| 164. #1290 | D53 | semidirect |
| 192. C53 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285728 | 2 |
| #20283793 | 2 |
| #20273408 | 2 |
| #20273352 | 2 |
| #20273117 | 2 |
| #20272576 | 2 |
| C53×#1290 | 2 |
| #9373 | 53 |