Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20290858 | C2 | semidirect |
| 4. C2×#16811482 | C2 | semidirect |
| 5. #20289606 | C2 | semidirect |
| 6. #20289559 | C2 | semidirect |
| 272. C53 | #9271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291459 | 2 |
| #20290858 | 2 |
| #20290227 | 2 |
| C2×#16811482 | 2 |
| #20289606 | 2 |
| #20289559 | 2 |
| #20285834 | 2 |
| #9271 | 53 |