Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
288 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #20272793 | C2 | semidirect |
| 28. C2×D4×C53 | C16 | semidirect |
| 105. C53 | #7102 | semidirect |
| 126. C2×D4 | #11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272793 | 2 |
| C53×#1954 | 2 |
| #7102 | 53 |