Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 1. C2×#16812139 | C2 | semidirect |
| 2. C2×C4×Dic214 | C2 | semidirect |
| 3. #20292846 | C2 | semidirect |
| 4. #20292834 | C2 | semidirect |
| 5. #20292824 | C2 | semidirect |
| 6. #20292651 | C2 | semidirect |
| 7. #20292628 | C2 | semidirect |
| 36. C2×Dic214 | D4 | semidirect |
| 110. C4×C107 | #137 | semidirect |
| 121. C107 | #3037 | semidirect |
| 233. C4 | #16812139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812139 | 2 |
| C2×C4×Dic214 | 2 |
| #20292846 | 2 |
| #20292834 | 2 |
| #20292824 | 2 |
| #20292651 | 2 |
| #20292628 | 2 |
| #532×C107 | 2 |
| #3037 | 107 |