Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
686 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20290115 | C2 | semidirect |
| 4. #20289995 | C2 | semidirect |
| 5. #20289587 | C2 | semidirect |
| 6. #20289557 | C2 | semidirect |
| 23. C22×#11719925 | C4 | semidirect |
| 29. C2×#13133142 | C4 | semidirect |
| 30. C2×#13133138 | C4 | semidirect |
| 32. C22×SD16×C53 | C4 | semidirect |
| 281. C22×SD16 | #6157 | semidirect |
| 304. C53 | #9239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291303 | 2 |
| #20290556 | 2 |
| #20290115 | 2 |
| #20289995 | 2 |
| #20289587 | 2 |
| #20289557 | 2 |
| C2×#16810782 | 2 |
| #9239 | 53 |