Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20292636 | C2 | semidirect |
| 4. #20292534 | C2 | semidirect |
| 5. #20292395 | C2 | semidirect |
| 6. #20292388 | C2 | semidirect |
| 24. #137×C107 | C4 | semidirect |
| 54. C2×Q8×C107 | C2×C4 | semidirect |
| 64. M16×C107 | C2×C4 | semidirect |
| 125. C107 | #1882 | semidirect |
| 136. #137 | Dic107 | semidirect |
| 162. C2×Q8 | C2×Dic107 | semidirect |
| 177. M16 | C2×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293110 | 2 |
| C2×#16812036 | 2 |
| #20292636 | 2 |
| #20292534 | 2 |
| #20292395 | 2 |
| #20292388 | 2 |
| C2×#137×C107 | 2 |
| #1882 | 107 |