Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20293105 | C2 | semidirect |
| 5. #20292399 | C2 | semidirect |
| 6. #20292383 | C2 | semidirect |
| 7. #419×C107 | C2 | semidirect |
| 11. C2×#13133808 | C4 | semidirect |
| 12. C2×#13133805 | C4 | semidirect |
| 110. C107 | #1905 | semidirect |
| 114. #419 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812140 | 2 |
| #20293105 | 2 |
| #20292643 | 2 |
| #20292600 | 2 |
| #20292399 | 2 |
| #20292383 | 2 |
| #419×C107 | 2 |
| #1905 | 107 |