Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20274765 | C2 | semidirect |
| 4. #20272843 | C2 | semidirect |
| 5. C53×#1812 | C2 | semidirect |
| 6. C22×C8×D53 | C4 | semidirect |
| 13. #16810651 | C4 | semidirect |
| 16. #16810586 | C4 | semidirect |
| 17. #16810578 | C4 | semidirect |
| 184. #1812 | D53 | semidirect |
| 211. C53 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283407 | 2 |
| #20276354 | 2 |
| #20274765 | 2 |
| #20272843 | 2 |
| C53×#1812 | 2 |
| #12805 | 53 |