Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 151 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×#16810401 | C2 | semidirect |
| 4. #20272794 | C2 | semidirect |
| 5. C2×C53×#347 | C2 | semidirect |
| 15. #16810402 | C4 | semidirect |
| 37. C2×#11719908 | C2×C4 | semidirect |
| 47. C2×C16×C53 | C2×C4 | semidirect |
| 123. C2×D53 | #347 | semidirect |
| 134. C2×#347 | D53 | semidirect |
| 155. C53 | #12605 | semidirect |
| 179. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D53 | 2 |
| #20276325 | 2 |
| C2×#16810401 | 2 |
| #20272794 | 2 |
| C2×C53×#347 | 2 |
| #12605 | 53 |