Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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. #20293036 | C2 | semidirect |
| 3. #20293032 | C2 | semidirect |
| 4. #20293029 | C2 | semidirect |
| 40. M16×C107 | Q8 | semidirect |
| 41. C2×C8×C107 | Q8 | semidirect |
| 81. C107 | #3164 | semidirect |
| 112. M16 | Dic214 | semidirect |
| 113. C2×C8 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20293036 | 2 |
| #20293032 | 2 |
| #20293029 | 2 |
| #20292669 | 2 |
| #20292665 | 2 |
| C2×#16812043 | 2 |
| #405×C107 | 2 |
| #3164 | 107 |