Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 35. #13133153 | Q8 | semidirect |
| 51. M32×C53 | Q8 | semidirect |
| 55. C2×C16×C53 | Q8 | semidirect |
| 158. C53 | #13456 | semidirect |
| 172. M32 | Dic106 | semidirect |
| 176. C2×C16 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285254 | 2 |
| #20276503 | 2 |
| C2×#16810451 | 2 |
| #20275500 | 2 |
| #20272824 | 2 |
| #20272811 | 2 |
| C53×#1379 | 2 |
| #13456 | 53 |