Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. C2×#16810445 | C2 | semidirect |
| 5. #20274888 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C2×C53×#365 | C2 | semidirect |
| 134. C2×#365 | D53 | semidirect |
| 160. C53 | #13535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810445 | 2 |
| C2×#16810437 | 2 |
| C2×#16810435 | 2 |
| #20275589 | 2 |
| #20274888 | 2 |
| #20272798 | 2 |
| C2×C53×#365 | 2 |
| #13535 | 53 |