Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #20292670 | C2 | direct (N × H) |
| 4. C2×#16812042 | C2 | semidirect |
| 5. C2×#16812040 | C2 | semidirect |
| 8. C2×#13133802 | C4 | semidirect |
| 15. #16812042 | C22 | semidirect |
| 16. #16812040 | C22 | semidirect |
| 27. #13133802 | C2×C4 | semidirect |
| 28. C2×C107⋊C8 | C2×C4 | semidirect |
| 69. C107⋊C8 | C22×C4 | semidirect |
| 86. C2×C107 | #428 | semidirect |
| 91. C107 | C2×#428 | semidirect |
| 177. C2 | #20292670 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133802 | 2 |
| C22×C4⋊Dic107 | 2 |
| #20292670 | 2 |
| C2×#16812042 | 2 |
| C2×#16812040 | 2 |
| C2×#117×C107 | 2 |
| C2×#428 | 107 |