Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 96 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. #20290435 | C2 | semidirect |
| 4. #20289923 | C2 | semidirect |
| 5. #20289609 | C2 | semidirect |
| 6. #20289604 | C2 | semidirect |
| 8. #16811674 | C4 | semidirect |
| 9. Q8×#88324 | C4 | semidirect |
| 10. #16811658 | C4 | semidirect |
| 13. D4×#88324 | C4 | semidirect |
| 29. #16810364 | C4 | semidirect |
| 30. #16810364 | C4 | semidirect |
| 31. #16810363 | C4 | semidirect |
| 32. C53×#329 | C4 | semidirect |
| 205. #329 | #6157 | semidirect |
| 210. C53 | #8248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291529 | 2 |
| #20290435 | 2 |
| #20290087 | 2 |
| #20289923 | 2 |
| #20289609 | 2 |
| #20289604 | 2 |
| #20273300 | 2 |
| #8248 | 53 |