Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
260 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20292653 | C2 | semidirect |
| 5. #20292398 | C2 | semidirect |
| 6. #20292397 | C2 | semidirect |
| 7. #424×C107 | C2 | semidirect |
| 93. C107 | #1868 | semidirect |
| 96. #424 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293393 | 2 |
| #20292653 | 2 |
| #20292600 | 2 |
| #20292593 | 2 |
| #20292398 | 2 |
| #20292397 | 2 |
| #424×C107 | 2 |
| #1868 | 107 |