Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 104 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×#16811547 | C2 | semidirect |
| 4. #20289780 | C2 | semidirect |
| 15. C2×#13133156 | C4 | semidirect |
| 16. C2×#13133156 | C4 | semidirect |
| 19. C22×#11719908 | C4 | semidirect |
| 20. C22×C16×C53 | C4 | semidirect |
| 80. C16×C53 | C22⋊C4 | semidirect |
| 82. #11719908 | C22⋊C4 | semidirect |
| 114. C22×C53 | #365 | semidirect |
| 147. C22×C16 | #6157 | semidirect |
| 155. C53 | #12831 | semidirect |
| 217. C16 | C22⋊#6157 | semidirect |
| 255. C22 | #16811547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811547 | 2 |
| #20290594 | 2 |
| #20290591 | 2 |
| #20289780 | 2 |
| C22×#13133156 | 2 |
| #12831 | 53 |