Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20290935 | C2 | semidirect |
| 4. #20290832 | C2 | semidirect |
| 5. #20289795 | C2 | semidirect |
| 6. #20289787 | C2 | semidirect |
| 23. #16810440 | C4 | semidirect |
| 24. #16810438 | C4 | semidirect |
| 25. #16810436 | C4 | semidirect |
| 26. C53×#361 | C4 | semidirect |
| 171. #361 | #6157 | semidirect |
| 177. C53 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811539 | 2 |
| #20290935 | 2 |
| #20290872 | 2 |
| #20290832 | 2 |
| #20289795 | 2 |
| #20289787 | 2 |
| #20276461 | 2 |
| #13156 | 53 |