Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
994 conjugacy classes of subgroups; only the 475 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 475 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 |
|---|---|---|
| 2. #20273017 | C2 | direct (N × H) |
| 3. C2×#16810344 | C2 | semidirect |
| 4. C2×C82×C53 | C2 | semidirect |
| 11. #16810344 | C22 | semidirect |
| 13. C82×C53 | C22 | semidirect |
| 34. C2×C8×C53 | M16 | semidirect |
| 53. C8×C53 | C2×M16 | semidirect |
| 66. C2×C82 | D53 | semidirect |
| 67. C2×C53 | #1455 | semidirect |
| 78. C82 | C2×D53 | semidirect |
| 79. C53 | C2×#1455 | semidirect |
| 103. C2×C8 | #11719912 | semidirect |
| 120. C8 | C2×#11719912 | semidirect |
| 129. C2 | #20273017 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719912 | 2 |
| #20273017 | 2 |
| C2×#16810344 | 2 |
| C2×C82×C53 | 2 |
| C2×#1455 | 53 |