Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 46. C4×Q8×C53 | C8 | semidirect |
| 181. C53 | #7596 | semidirect |
| 186. C4×Q8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290642 | 2 |
| #20290630 | 2 |
| #20289535 | 2 |
| #20289533 | 2 |
| #20277193 | 2 |
| #7596 | 53 |