Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
210 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 81. C8×C53 | Q32 | semidirect |
| 122. C53 | #12072 | semidirect |
| 183. C8 | Dic424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic424 | 2 |
| #20273613 | 2 |
| C8×Dic212 | 2 |
| #20272787 | 2 |
| #20272680 | 2 |
| C53×#1312 | 2 |
| #12072 | 53 |