Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C2×#16811032 | C2 | semidirect |
| 4. #20275687 | C2 | semidirect |
| 5. C2×#16810364 | C2 | semidirect |
| 7. C53×#1295 | C2 | semidirect |
| 195. #1295 | D53 | semidirect |
| 225. C53 | #10082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811032 | 2 |
| C2×#16811017 | 2 |
| #20282767 | 2 |
| #20275687 | 2 |
| C2×#16810364 | 2 |
| C2×#16810362 | 2 |
| C53×#1295 | 2 |
| #10082 | 53 |