Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20274853 | C2 | semidirect |
| 4. #20272611 | C2 | semidirect |
| 5. C53×#1564 | C2 | semidirect |
| 134. #1564 | D53 | semidirect |
| 158. C53 | #8660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D212 | 2 |
| #20274853 | 2 |
| #20273141 | 2 |
| #20272611 | 2 |
| C53×#1564 | 2 |
| #8660 | 53 |