Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20293030 | C2 | semidirect |
| 3. #20293006 | C2 | semidirect |
| 4. #20292979 | C2 | semidirect |
| 5. #20292977 | C2 | semidirect |
| 7. C4×#13133808 | C2 | semidirect |
| 73. C2×C4×C107 | Q16 | semidirect |
| 105. C107 | #3170 | semidirect |
| 182. C2×C4 | #13133808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| #20293030 | 2 |
| #20293006 | 2 |
| #20292979 | 2 |
| #20292977 | 2 |
| #20292866 | 2 |
| C4×#13133808 | 2 |
| C2×C4×C107⋊C8 | 2 |
| #533×C107 | 2 |
| #3170 | 107 |