Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #20293032 | C2 | semidirect |
| 2. #20293030 | C2 | semidirect |
| 3. #20293006 | C2 | semidirect |
| 6. #20292349 | C2 | semidirect |
| 70. C107 | #1722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293032 | 2 |
| #20293030 | 2 |
| #20293006 | 2 |
| #20292999 | 2 |
| #20292973 | 2 |
| #20292349 | 2 |
| #486×C107 | 2 |
| #1722 | 107 |