Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
948 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 114 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×#16811540 | C2 | semidirect |
| 2. #20290943 | C2 | semidirect |
| 3. #20290591 | C2 | semidirect |
| 5. C2×#13133292 | C22 | semidirect |
| 6. C2×#13133285 | C22 | semidirect |
| 16. C2×#13133240 | C4 | semidirect |
| 19. C22×D424 | C4 | semidirect |
| 21. C22×Q16×C53 | C4 | semidirect |
| 98. Q16×C53 | C22⋊C4 | semidirect |
| 109. D424 | C22⋊C4 | semidirect |
| 160. C22×C53 | #360 | semidirect |
| 197. C22×Q16 | #6157 | semidirect |
| 208. C53 | #12735 | semidirect |
| 282. Q16 | C22⋊#6157 | semidirect |
| 357. C22 | #16811540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811540 | 2 |
| #20290943 | 2 |
| #20290591 | 2 |
| C22×#13133240 | 2 |
| #12735 | 53 |