Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16810456 | C2 | semidirect |
| 3. #366×D53 | C2 | semidirect |
| 4. #20272896 | C2 | semidirect |
| 5. #20272894 | C2 | semidirect |
| 6. #20272892 | C2 | semidirect |
| 7. C53×#1416 | C2 | semidirect |
| 10. #16811056 | C4 | semidirect |
| 31. D848 | C2×C4 | semidirect |
| 40. Q32×C53 | C2×C4 | semidirect |
| 104. #1416 | D53 | semidirect |
| 126. C53 | #13616 | semidirect |
| 136. Q32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811056 | 2 |
| C2×#16810456 | 2 |
| #366×D53 | 2 |
| #20272896 | 2 |
| #20272894 | 2 |
| #20272892 | 2 |
| C53×#1416 | 2 |
| #13616 | 53 |