Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
872 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 237 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. #20292529 | C2 | semidirect |
| 4. #20292527 | C2 | semidirect |
| 5. #20292487 | C2 | semidirect |
| 6. #20292486 | C2 | semidirect |
| 7. #20292474 | C2 | semidirect |
| 8. C4×C22⋊C4×C107 | C2 | semidirect |
| 10. C2×#13133818 | C4 | semidirect |
| 76. C2×C4×C107 | #41 | semidirect |
| 85. Dic214 | C22⋊C4 | semidirect |
| 115. C107 | #2341 | semidirect |
| 123. C4×C22⋊C4 | D107 | semidirect |
| 200. C2×C4 | #13133818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133818 | 2 |
| C2×C4×Dic214 | 2 |
| #20292529 | 2 |
| #20292527 | 2 |
| #20292487 | 2 |
| #20292486 | 2 |
| #20292474 | 2 |
| C4×C22⋊C4×C107 | 2 |
| #2341 | 107 |