Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
644 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20274650 | C2 | semidirect |
| 3. #20274639 | C2 | semidirect |
| 5. #20272622 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 28. C53×#451 | C4 | semidirect |
| 30. C53×#448 | C4 | semidirect |
| 262. #451 | Dic53 | semidirect |
| 264. #448 | Dic53 | semidirect |
| 283. C53 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283763 | 2 |
| #20274650 | 2 |
| #20274639 | 2 |
| #20273258 | 2 |
| #20272622 | 2 |
| #20272591 | 2 |
| C53×#3004 | 2 |
| #9519 | 53 |