Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 29. C4⋊Q8×C53 | C8 | semidirect |
| 115. C53 | #7571 | semidirect |
| 119. C4⋊Q8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#88324 | 2 |
| #20289535 | 2 |
| C4⋊Q8×Dic53 | 2 |
| #7571 | 53 |