Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 10. #16811514 | C4 | direct (N × H) |
| 11. #16811512 | C4 | semidirect |
| 12. C4×#11719910 | C4 | semidirect |
| 15. #16810398 | C4 | semidirect |
| 16. C4×#11719908 | C4 | semidirect |
| 17. C4×C16×C53 | C4 | semidirect |
| 54. #11719910 | C42 | semidirect |
| 55. C16×C53 | C42 | semidirect |
| 56. #11719908 | C42 | semidirect |
| 77. C4×C53 | #347 | semidirect |
| 101. C4×C16 | #6157 | semidirect |
| 102. C53 | C4×#347 | semidirect |
| 141. C16 | C4×#6157 | semidirect |
| 163. C4 | #16811514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811514 | 2 |
| C4×#13133292 | 2 |
| C4×#13133271 | 2 |
| C4×#13133156 | 2 |
| C4×#347 | 53 |