Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×Dic214 | C2 | semidirect |
| 3. C2×#16812034 | C2 | semidirect |
| 6. #20292390 | C2 | semidirect |
| 7. #336×C107 | C2 | semidirect |
| 12. C2×#13133807 | C4 | semidirect |
| 75. C2×C4×C107 | SD16 | semidirect |
| 98. Dic214 | C22⋊C4 | semidirect |
| 133. C107 | #1880 | semidirect |
| 140. #336 | D107 | semidirect |
| 225. C2×C4 | #13133807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133807 | 2 |
| C2×C4×Dic214 | 2 |
| C2×#16812034 | 2 |
| C2×#16812031 | 2 |
| #20292529 | 2 |
| #20292390 | 2 |
| #336×C107 | 2 |
| #1880 | 107 |