Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 17. #16810399 | C4 | semidirect |
| 18. #16810398 | C4 | semidirect |
| 19. C53×#346 | C4 | semidirect |
| 65. C16×C53 | C4⋊C4 | semidirect |
| 66. #11719908 | C4⋊C4 | semidirect |
| 126. #346 | #6157 | semidirect |
| 127. C53 | #12908 | semidirect |
| 174. C16 | C4⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811550 | 2 |
| C2×#16811549 | 2 |
| #20290652 | 2 |
| #20290651 | 2 |
| #346×D53 | 2 |
| #12908 | 53 |