Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
370 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 21. C2×Dic212 | Q8 | semidirect |
| 128. C53 | #13368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276434 | 2 |
| #20275586 | 2 |
| #20272820 | 2 |
| #20272799 | 2 |
| C53×#3162 | 2 |
| #13368 | 53 |