Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20292396 | C2 | semidirect |
| 4. #20292386 | C2 | semidirect |
| 5. #544×C107 | C2 | semidirect |
| 21. C2×D428 | Q8 | semidirect |
| 82. C107 | #2027 | semidirect |
| 83. #544 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292631 | 2 |
| #20292528 | 2 |
| #20292396 | 2 |
| #20292386 | 2 |
| #544×C107 | 2 |
| #2027 | 107 |