Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20272668 | C2 | semidirect |
| 4. #20272667 | C2 | semidirect |
| 5. C53×#1328 | C2 | semidirect |
| 139. #1328 | D53 | direct (N × H) |
| 145. D53 | #1328 | direct (N × H) |
| 159. C53 | C2×#1328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #424×D53 | 2 |
| #349×D53 | 2 |
| #20272668 | 2 |
| #20272667 | 2 |
| C53×#1328 | 2 |
| C2×#1328 | 53 |