Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #20292675 | C2 | semidirect |
| 5. M16×Dic107 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #344×C107 | C2 | semidirect |
| 16. #16812027 | C4 | semidirect |
| 17. #16812025 | C4 | semidirect |
| 96. C107 | #1932 | semidirect |
| 102. #344 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292675 | 2 |
| #20292645 | 2 |
| C2×#16812035 | 2 |
| #20292609 | 2 |
| M16×Dic107 | 2 |
| #20292386 | 2 |
| #344×C107 | 2 |
| #1932 | 107 |