Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 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×C22⋊(C107⋊C8) | C2 | semidirect |
| 3. #20292360 | C2 | semidirect |
| 4. #380×C107 | C2 | semidirect |
| 5. C22×D428 | C4 | semidirect |
| 10. #16812083 | C4 | semidirect |
| 12. C2×C4⋊Dic107 | C4 | semidirect |
| 15. C22⋊(C107⋊C8) | C22 | semidirect |
| 19. #95×C107 | C22 | semidirect |
| 110. C107 | #1519 | semidirect |
| 113. #380 | D107 | semidirect |
| 129. #95 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812083 | 2 |
| C2×C22⋊(C107⋊C8) | 2 |
| #20292360 | 2 |
| #380×C107 | 2 |
| #1519 | 107 |