Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1170 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20274477 | C2 | semidirect |
| 3. C2×#16810362 | C2 | semidirect |
| 4. C53×#1749 | C2 | semidirect |
| 15. C2×#13133128 | C22 | semidirect |
| 20. C2×#97×C53 | C22 | semidirect |
| 180. C22×C53 | #329 | semidirect |
| 205. #1749 | D53 | semidirect |
| 229. C2×#97 | C2×D53 | semidirect |
| 233. C53 | #8334 | semidirect |
| 399. C22 | #16810362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133205 | 2 |
| #20274477 | 2 |
| C2×#16810362 | 2 |
| C53×#1749 | 2 |
| #8334 | 53 |