Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20292686 | C2 | semidirect |
| 3. #20292682 | C2 | semidirect |
| 4. #20292655 | C2 | semidirect |
| 6. C2×#16812020 | C2 | semidirect |
| 7. C4×M16×C107 | C2 | semidirect |
| 78. C107 | #2923 | semidirect |
| 84. C4×M16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133818 | 2 |
| #20292686 | 2 |
| #20292682 | 2 |
| #20292655 | 2 |
| #20292595 | 2 |
| C2×#16812020 | 2 |
| C4×M16×C107 | 2 |
| #2923 | 107 |