Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812142 | C2 | semidirect |
| 3. #20293198 | C2 | semidirect |
| 4. #20292885 | C2 | semidirect |
| 5. #20292873 | C2 | semidirect |
| 6. #20292868 | C2 | semidirect |
| 7. #20292856 | C2 | semidirect |
| 8. #20292669 | C2 | semidirect |
| 9. #20292624 | C2 | semidirect |
| 10. C2×#16812034 | C2 | semidirect |
| 11. C2×#131×C107 | C2 | semidirect |
| 79. M16×C107 | D4 | semidirect |
| 144. C107 | #3063 | semidirect |
| 146. C2×#131 | D107 | semidirect |
| 210. M16 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812142 | 2 |
| #20293205 | 2 |
| #20293198 | 2 |
| #20292885 | 2 |
| #20292873 | 2 |
| #20292868 | 2 |
| #20292856 | 2 |
| #20292669 | 2 |
| #20292624 | 2 |
| C2×#16812034 | 2 |
| C2×#131×C107 | 2 |
| #3063 | 107 |