Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
310 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 310 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 |
|---|---|---|
| 37. #13133153 | Q8 | semidirect |
| 52. M32×C53 | Q8 | semidirect |
| 54. C2×C16×C53 | Q8 | semidirect |
| 150. C53 | #13460 | semidirect |
| 166. M32 | Dic106 | semidirect |
| 168. C2×C16 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285246 | 2 |
| #20276488 | 2 |
| C2×#16810446 | 2 |
| #20275505 | 2 |
| #20272830 | 2 |
| #20272814 | 2 |
| C53×#1378 | 2 |
| #13460 | 53 |