Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
320 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 117 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. M16×Dic107 | C2 | semidirect |
| 4. #20292473 | C2 | semidirect |
| 5. #20292388 | C2 | semidirect |
| 6. #20292387 | C2 | semidirect |
| 9. Q8×Dic107 | C4 | semidirect |
| 11. D4×Dic107 | C4 | semidirect |
| 17. #16812036 | C4 | semidirect |
| 24. #104×C107 | C4 | semidirect |
| 29. #13133802 | C2×C4 | semidirect |
| 39. C4×Dic107 | C2×C4 | semidirect |
| 53. M16×C107 | C2×C4 | semidirect |
| 56. C42×C107 | C2×C4 | semidirect |
| 107. C107 | #1759 | semidirect |
| 128. #104 | Dic107 | semidirect |
| 148. M16 | C2×Dic107 | semidirect |
| 163. C42 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic107 | 2 |
| C2×#16812036 | 2 |
| M16×Dic107 | 2 |
| #20292473 | 2 |
| #20292388 | 2 |
| #20292387 | 2 |
| C2×#104×C107 | 2 |
| #1759 | 107 |