Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #20289881 | C2 | direct (N × H) |
| 12. #16810456 | C4 | semidirect |
| 14. C2×#13133123 | C4 | semidirect |
| 15. C2×C32×C53 | C4 | semidirect |
| 28. #13133123 | C2×C4 | semidirect |
| 30. C32×C53 | C2×C4 | semidirect |
| 76. C2×C53 | #1426 | semidirect |
| 86. C2×C32 | #6157 | semidirect |
| 91. C53 | C2×#1426 | semidirect |
| 106. C32 | C2×#6157 | semidirect |
| 149. C2 | #20289881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811552 | 2 |
| C2×#16811550 | 2 |
| #20289881 | 2 |
| C2×#16810456 | 2 |
| C2×#1426 | 53 |