Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 10. #16810451 | C4 | semidirect |
| 11. #16810449 | C4 | semidirect |
| 105. C53 | #13169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810453 | 2 |
| #20276499 | 2 |
| #20275463 | 2 |
| #20272811 | 2 |
| C2×C4×C16×C53 | 2 |
| #13169 | 53 |