Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#16812031 | C2 | semidirect |
| 3. C2×#16812030 | C2 | semidirect |
| 4. C2×#16812029 | C2 | semidirect |
| 5. #20292526 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 7. C2×#102×C107 | C2 | semidirect |
| 62. C4⋊C4×C107 | D4 | semidirect |
| 147. C107 | #2041 | semidirect |
| 152. C2×#102 | D107 | semidirect |
| 207. C4⋊C4 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812105 | 2 |
| C2×#16812031 | 2 |
| C2×#16812030 | 2 |
| C2×#16812029 | 2 |
| #20292526 | 2 |
| #20292381 | 2 |
| C2×#102×C107 | 2 |
| #2041 | 107 |