Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 118 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×#16811549 | C2 | semidirect |
| 3. #20289773 | C2 | semidirect |
| 10. C22×#11719908 | C4 | semidirect |
| 12. C2×C16×D53 | C4 | semidirect |
| 13. C2×C16×D53 | C4 | semidirect |
| 16. C22×C16×C53 | C4 | semidirect |
| 68. C16×C53 | C22⋊C4 | semidirect |
| 70. #11719908 | C22⋊C4 | semidirect |
| 102. C22×C53 | #366 | semidirect |
| 108. C2×D53 | #366 | semidirect |
| 137. C22×C16 | #6157 | semidirect |
| 142. C53 | #12834 | semidirect |
| 196. C16 | C22⋊#6157 | semidirect |
| 236. C22 | #16811549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811549 | 2 |
| #20290592 | 2 |
| #20289773 | 2 |
| C22×C16×D53 | 2 |
| #12834 | 53 |