Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#13133808 | C2 | semidirect |
| 4. #20292781 | C2 | direct (N × H) |
| 5. C2×#16812034 | C2 | semidirect |
| 6. C2×#16812033 | C2 | semidirect |
| 8. C22×Q16×C107 | C2 | semidirect |
| 18. C2×#13133808 | C22 | semidirect |
| 25. #16812034 | C22 | semidirect |
| 26. #16812033 | C22 | semidirect |
| 31. C2×Q16×C107 | C22 | semidirect |
| 76. C22×D107 | Q16 | semidirect |
| 115. C2×D107 | C2×Q16 | semidirect |
| 124. C2×C107 | #451 | semidirect |
| 130. C107 | C2×#451 | semidirect |
| 133. C22×Q16 | D107 | semidirect |
| 152. C2×Q16 | C2×D107 | semidirect |
| 255. C2 | #20292781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D107 | 2 |
| C22×#13133808 | 2 |
| C2×#16812085 | 2 |
| #20292781 | 2 |
| C2×#16812034 | 2 |
| C2×#16812033 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C22×Q16×C107 | 2 |
| C2×#451 | 107 |