Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #20292637 | C2 | semidirect |
| 5. #20292532 | C2 | semidirect |
| 6. #20292388 | C2 | semidirect |
| 7. #343×C107 | C2 | semidirect |
| 11. #16812142 | C4 | semidirect |
| 37. C2×Dic214 | C2×C4 | semidirect |
| 61. M16×C107 | C2×C4 | semidirect |
| 125. C107 | #1882 | semidirect |
| 131. #343 | D107 | semidirect |
| 177. M16 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812142 | 2 |
| #20293108 | 2 |
| C2×#16812035 | 2 |
| #20292637 | 2 |
| #20292532 | 2 |
| #20292388 | 2 |
| #343×C107 | 2 |
| #1882 | 107 |