Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 11. #16811023 | C4 | semidirect |
| 12. #16811020 | C4 | semidirect |
| 33. #13133157 | Q8 | semidirect |
| 49. C2×C16×C53 | Q8 | semidirect |
| 146. C53 | #13291 | semidirect |
| 164. C2×C16 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285243 | 2 |
| #20276319 | 2 |
| #20274840 | 2 |
| #20272829 | 2 |
| #20272822 | 2 |
| #20272817 | 2 |
| C53×#1383 | 2 |
| #13291 | 53 |