Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. C2×#16811513 | C2 | semidirect |
| 4. #20290530 | C2 | semidirect |
| 5. #20289789 | C2 | semidirect |
| 6. #20289780 | C2 | semidirect |
| 11. #16811669 | C4 | semidirect |
| 17. #16811540 | C4 | semidirect |
| 23. #16810427 | C4 | semidirect |
| 24. #16810425 | C4 | semidirect |
| 25. #16810423 | C4 | semidirect |
| 26. C53×#358 | C4 | semidirect |
| 90. Q16×C53 | C42 | semidirect |
| 99. D424 | C42 | semidirect |
| 185. #358 | #6157 | semidirect |
| 190. C53 | #12650 | semidirect |
| 241. Q16 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811669 | 2 |
| C2×#16811540 | 2 |
| C2×#16811513 | 2 |
| #20290530 | 2 |
| #20289789 | 2 |
| #20289780 | 2 |
| #20276426 | 2 |
| #12650 | 53 |