Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
728 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20275692 | C2 | semidirect |
| 4. #20273453 | C2 | semidirect |
| 5. #20273452 | C2 | semidirect |
| 7. C53×#1994 | C2 | semidirect |
| 8. #16811377 | C4 | semidirect |
| 223. #1994 | D53 | semidirect |
| 259. C53 | #8531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289126 | 2 |
| #20275692 | 2 |
| #20275543 | 2 |
| #20273453 | 2 |
| #20273452 | 2 |
| #20273448 | 2 |
| C53×#1994 | 2 |
| #8531 | 53 |