Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291683 | C2 | semidirect |
| 2. C2×#16811541 | C2 | semidirect |
| 3. #20291024 | C2 | semidirect |
| 4. #20290601 | C2 | semidirect |
| 5. #20289795 | C2 | semidirect |
| 6. #20289784 | C2 | semidirect |
| 25. #16810894 | C4 | semidirect |
| 26. #16810893 | C4 | semidirect |
| 29. #16810890 | C4 | semidirect |
| 32. C53×#472 | C4 | semidirect |
| 246. #472 | #6157 | semidirect |
| 256. C53 | #13068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291683 | 2 |
| C2×#16811541 | 2 |
| #20291024 | 2 |
| #20290601 | 2 |
| #20289795 | 2 |
| #20289784 | 2 |
| #472×D53 | 2 |
| #13068 | 53 |