Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 139 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. C4×#13133136 | C2 | semidirect |
| 3. #20272842 | C2 | semidirect |
| 7. #16810420 | C4 | direct (N × H) |
| 20. #13133136 | C2×C4 | semidirect |
| 139. C4×C53 | #355 | semidirect |
| 163. C53 | C4×#355 | semidirect |
| 284. C4 | #16810420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810420 | 2 |
| C4×#13133136 | 2 |
| #20272842 | 2 |
| C4×#124×C53 | 2 |
| C4×#355 | 53 |