Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
360 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#16812019 | C2 | semidirect |
| 5. #20292382 | C2 | semidirect |
| 6. #20292381 | C2 | semidirect |
| 7. C2×#97×C107 | C2 | semidirect |
| 13. C2×C8×D107 | C4 | semidirect |
| 16. (C2×D107)⋊C8 | C4 | semidirect |
| 78. C8×C107 | C22⋊C4 | semidirect |
| 90. C2×D107 | #97 | semidirect |
| 105. C107 | #1752 | semidirect |
| 109. C2×#97 | D107 | semidirect |
| 185. C8 | (C2×D107)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D107 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| C2×#16812019 | 2 |
| C4×(C2×D107)⋊C4 | 2 |
| #20292382 | 2 |
| #20292381 | 2 |
| C2×#97×C107 | 2 |
| #1752 | 107 |