Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
774 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 297 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. C2×#16812116 | C2 | semidirect |
| 2. #20292594 | C2 | semidirect |
| 3. #20292591 | C2 | semidirect |
| 4. C2×C22⋊(C107⋊C8) | C2 | semidirect |
| 7. C2×#13133802 | C22 | semidirect |
| 8. C22×C107⋊C8 | C22 | semidirect |
| 11. C22⋊(C107⋊C8) | C22 | semidirect |
| 12. C22⋊(C107⋊C8) | C22 | semidirect |
| 76. C22×C107 | #131 | semidirect |
| 89. C107 | #2880 | semidirect |
| 165. C22 | #16812116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812116 | 2 |
| #20292594 | 2 |
| #20292591 | 2 |
| C2×C22⋊(C107⋊C8) | 2 |
| C22×#41×C107 | 2 |
| #2880 | 107 |