Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20274812 | C2 | semidirect |
| 4. #20274790 | C2 | semidirect |
| 5. #20272624 | C2 | semidirect |
| 6. #20272567 | C2 | semidirect |
| 10. #16810939 | C4 | semidirect |
| 11. #16810934 | C4 | semidirect |
| 38. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 39. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 56. C22⋊#88322 | C2×C4 | semidirect |
| 262. C53 | #9525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284651 | 2 |
| #20277482 | 2 |
| #20274812 | 2 |
| #20274790 | 2 |
| #20272624 | 2 |
| #20272567 | 2 |
| C53×#1510 | 2 |
| #9525 | 53 |