Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. C2×#16811536 | C2 | semidirect |
| 4. #20289772 | C2 | semidirect |
| 17. #16810865 | C4 | semidirect |
| 18. #16810864 | C4 | semidirect |
| 21. #16810861 | C4 | semidirect |
| 24. C53×#467 | C4 | semidirect |
| 157. C22×C53 | #358 | semidirect |
| 163. C2×D53 | #358 | semidirect |
| 202. #467 | #6157 | semidirect |
| 209. C53 | #13060 | semidirect |
| 350. C22 | #16811536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D53⋊C16 | 2 |
| C2×#16811536 | 2 |
| #20290592 | 2 |
| #20289772 | 2 |
| #467×D53 | 2 |
| #13060 | 53 |