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. #20292655 | C2 | semidirect |
| 3. #20292654 | C2 | semidirect |
| 6. #20292399 | C2 | semidirect |
| 7. #344×C107 | C2 | semidirect |
| 93. C107 | #1868 | semidirect |
| 100. #344 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293393 | 2 |
| #20292655 | 2 |
| #20292654 | 2 |
| #20292600 | 2 |
| #20292595 | 2 |
| #20292399 | 2 |
| #344×C107 | 2 |
| #1868 | 107 |