Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 7. #16811529 | C4 | semidirect |
| 9. #16811479 | C4 | semidirect |
| 12. C2×#13133136 | C4 | semidirect |
| 14. C53×#519 | C4 | semidirect |
| 127. #519 | #6157 | semidirect |
| 137. C53 | #7489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811529 | 2 |
| C2×#16811479 | 2 |
| #20275118 | 2 |
| #7489 | 53 |