Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 578 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 |
|---|---|---|
| 1. C22×D53⋊C16 | C2 | semidirect |
| 2. C2×#16811535 | C2 | semidirect |
| 3. #20290592 | C2 | semidirect |
| 4. #20289772 | C2 | semidirect |
| 17. #16810860 | C4 | semidirect |
| 18. #16810859 | C4 | semidirect |
| 21. #16810856 | C4 | semidirect |
| 24. C53×#466 | C4 | semidirect |
| 29. D53⋊C16 | D4 | semidirect |
| 170. C22×C53 | #357 | semidirect |
| 181. C2×D53 | #357 | semidirect |
| 220. #466 | #6157 | semidirect |
| 227. C53 | #13059 | semidirect |
| 386. C22 | #16811535 | 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×#16811535 | 2 |
| #20290592 | 2 |
| #20289772 | 2 |
| #466×D53 | 2 |
| #13059 | 53 |