Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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. #20292566 | C2 | semidirect |
| 3. #20292553 | C2 | semidirect |
| 5. #20292538 | C2 | semidirect |
| 6. C4×(C2×D107)⋊C4 | C2 | semidirect |
| 7. #20292473 | C2 | semidirect |
| 8. C2×C4×Q8×C107 | C2 | semidirect |
| 97. C107 | #2398 | semidirect |
| 98. C2×C4×Q8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D428 | 2 |
| #20292566 | 2 |
| #20292553 | 2 |
| #20292544 | 2 |
| #20292538 | 2 |
| C4×(C2×D107)⋊C4 | 2 |
| #20292473 | 2 |
| C2×C4×Q8×C107 | 2 |
| #2398 | 107 |