Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1050 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 219 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. #20277438 | C2 | semidirect |
| 3. #20275538 | C2 | semidirect |
| 4. #20275064 | C2 | semidirect |
| 5. #20274466 | C2 | semidirect |
| 6. C53×#1835 | C2 | semidirect |
| 10. #16811000 | C4 | semidirect |
| 24. C2×D424 | C2×C4 | semidirect |
| 27. #13133214 | C2×C4 | semidirect |
| 38. C4×C8×C53 | C2×C4 | semidirect |
| 103. #1835 | D53 | semidirect |
| 122. C53 | #22276 | semidirect |
| 140. C4×C8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| #20277438 | 2 |
| #20275538 | 2 |
| #20275064 | 2 |
| #20274466 | 2 |
| C53×#1835 | 2 |
| #22276 | 53 |