Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
362 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20292934 | C2 | semidirect |
| 3. #20292934 | C2 | semidirect |
| 4. #20292922 | C2 | semidirect |
| 5. #20292912 | C2 | semidirect |
| 59. C2×Q8×C107 | Q8 | semidirect |
| 117. C107 | #3082 | semidirect |
| 161. C2×Q8 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20292934 | 2 |
| #20292922 | 2 |
| #20292912 | 2 |
| #20292670 | 2 |
| #20292663 | 2 |
| #20292654 | 2 |
| #20292636 | 2 |
| C2×#16812033 | 2 |
| #519×C107 | 2 |
| #3082 | 107 |