Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 28. #13133217 | Q8 | semidirect |
| 29. #13133217 | Q8 | semidirect |
| 191. C53 | #10379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275658 | 2 |
| #20273265 | 2 |
| #20273226 | 2 |
| #20272608 | 2 |
| #20272579 | 2 |
| #20272571 | 2 |
| C53×#2605 | 2 |
| #10379 | 53 |