Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 15. #16810450 | C4 | semidirect |
| 16. #16810448 | C4 | semidirect |
| 133. C53 | #13169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810452 | 2 |
| #20276497 | 2 |
| C2×C16×Dic53 | 2 |
| #20275464 | 2 |
| #20275461 | 2 |
| #20272811 | 2 |
| C53×#1382 | 2 |
| #13169 | 53 |