Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 22. C2×Dic212 | Q8 | semidirect |
| 144. C53 | #13364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811028 | 2 |
| C2×#16810428 | 2 |
| #20275576 | 2 |
| #20272807 | 2 |
| C53×#1374 | 2 |
| #13364 | 53 |