Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×Dic107⋊C8 | C2 | semidirect |
| 5. #20292382 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 7. C2×C4⋊C8×C107 | C2 | semidirect |
| 70. C2×C4×C107 | M16 | semidirect |
| 85. C2×Dic107 | M16 | semidirect |
| 126. C107 | #1851 | semidirect |
| 129. C2×C4⋊C8 | D107 | semidirect |
| 209. C2×C4 | #13133801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133801 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C4×(C2×D107)⋊C4 | 2 |
| #20292382 | 2 |
| #20292381 | 2 |
| C2×C4⋊C8×C107 | 2 |
| #1851 | 107 |