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. #16811670 | C4 | semidirect |
| 17. #16811539 | C4 | semidirect |
| 23. #16810428 | C4 | semidirect |
| 24. #16810426 | C4 | semidirect |
| 25. #16810424 | C4 | semidirect |
| 26. C53×#357 | C4 | semidirect |
| 90. D8×C53 | C42 | semidirect |
| 99. Dic212 | C42 | semidirect |
| 187. #357 | #6157 | semidirect |
| 190. C53 | #12650 | semidirect |
| 245. D8 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811670 | 2 |
| C2×#16811539 | 2 |
| C2×#16811513 | 2 |
| #20290530 | 2 |
| #20289789 | 2 |
| #20289780 | 2 |
| #20276424 | 2 |
| #12650 | 53 |