Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20289772 | C2 | semidirect |
| 4. #20289772 | C2 | semidirect |
| 14. #16810661 | C4 | semidirect |
| 15. #16810660 | C4 | semidirect |
| 16. #16810660 | C4 | semidirect |
| 22. C53×#427 | C4 | semidirect |
| 175. #427 | #6157 | semidirect |
| 184. C53 | #12868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290592 | 2 |
| #20289772 | 2 |
| #427×D53 | 2 |
| #12868 | 53 |