Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#16812131 | C2 | semidirect |
| 2. C2×#16812129 | C2 | semidirect |
| 3. #20293173 | C2 | semidirect |
| 4. #20293020 | C2 | semidirect |
| 5. #20293018 | C2 | semidirect |
| 6. #20293015 | C2 | semidirect |
| 7. #20293013 | C2 | semidirect |
| 8. C2×#16812019 | C2 | semidirect |
| 9. C2×#135×C107 | C2 | semidirect |
| 51. C2×C107⋊C8 | D4 | semidirect |
| 68. C2×C8×C107 | D4 | semidirect |
| 117. C107 | #3150 | semidirect |
| 120. C2×#135 | D107 | semidirect |
| 180. C2×C8 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| C2×#16812129 | 2 |
| #20293173 | 2 |
| #20293020 | 2 |
| #20293018 | 2 |
| #20293015 | 2 |
| #20293013 | 2 |
| C2×#16812019 | 2 |
| C2×#135×C107 | 2 |
| #3150 | 107 |