Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
672 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16810563 | C2 | semidirect |
| 4. #20274806 | C2 | semidirect |
| 5. C2×#16810348 | C2 | semidirect |
| 6. #20272594 | C2 | semidirect |
| 270. C53 | #9921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810939 | 2 |
| #20280459 | 2 |
| C2×#16810563 | 2 |
| #20274806 | 2 |
| C2×#16810348 | 2 |
| #20272594 | 2 |
| C2×C53×#327 | 2 |
| #9921 | 53 |