Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×C8×Dic107 | C2 | semidirect |
| 5. #20292382 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 7. C2×C4×C8×C107 | C2 | semidirect |
| 13. C2×C8×D107 | C4 | semidirect |
| 16. (C2×D107)⋊C8 | C4 | semidirect |
| 39. (C2×D107)⋊C4 | C8 | direct (N × H) |
| 60. C2×C4×C107 | C2×C8 | semidirect |
| 72. C2×Dic107 | C2×C8 | semidirect |
| 78. C8×C107 | C22⋊C4 | semidirect |
| 90. C2×D107 | C4×C8 | semidirect |
| 105. C107 | C8×C22⋊C4 | semidirect |
| 109. C2×C4×C8 | D107 | semidirect |
| 175. C2×C4 | C8×D107 | semidirect |
| 185. C8 | (C2×D107)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D107 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C2×C8×Dic107 | 2 |
| C4×(C2×D107)⋊C4 | 2 |
| #20292382 | 2 |
| #20292381 | 2 |
| C2×C4×C8×C107 | 2 |
| C8×C22⋊C4 | 107 |