Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20290657 | C2 | semidirect |
| 3. #20290280 | C2 | semidirect |
| 5. #20289609 | C2 | semidirect |
| 6. #20289600 | C2 | semidirect |
| 199. C53 | #8916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291673 | 2 |
| #20290657 | 2 |
| #20290280 | 2 |
| #20290073 | 2 |
| #20289609 | 2 |
| #20289600 | 2 |
| #20273302 | 2 |
| #8916 | 53 |