Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 91 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×C32×D53 | C2 | semidirect |
| 3. #366×D53 | C2 | semidirect |
| 4. #20272894 | C2 | semidirect |
| 5. #20272893 | C2 | semidirect |
| 6. #20272892 | C2 | semidirect |
| 7. C53×#1415 | C2 | semidirect |
| 12. D16×D53 | C4 | semidirect |
| 15. C2×#13133123 | C22 | semidirect |
| 17. #16810449 | C22 | semidirect |
| 20. C2×C32×C53 | C22 | semidirect |
| 21. C53×#366 | C22 | semidirect |
| 30. D848 | C2×C4 | semidirect |
| 40. D16×C53 | C2×C4 | semidirect |
| 111. #1415 | D53 | direct (N × H) |
| 117. D53 | #1415 | direct (N × H) |
| 128. C2×C32 | C2×D53 | semidirect |
| 131. #366 | C2×D53 | semidirect |
| 132. C53 | C2×#1415 | semidirect |
| 145. D16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D53 | 2 |
| C2×C32×D53 | 2 |
| #366×D53 | 2 |
| #20272894 | 2 |
| #20272893 | 2 |
| #20272892 | 2 |
| C53×#1415 | 2 |
| C2×#1415 | 53 |