Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16812141 | C2 | semidirect |
| 3. C2×Q16×D107 | C2 | semidirect |
| 4. #20293202 | C2 | semidirect |
| 5. #20293020 | C2 | semidirect |
| 6. #20293019 | C2 | semidirect |
| 7. #20293012 | C2 | semidirect |
| 8. #20293011 | C2 | semidirect |
| 9. #20293005 | C2 | semidirect |
| 10. #20292581 | C2 | semidirect |
| 11. #494×C107 | C2 | semidirect |
| 122. C107 | #3156 | semidirect |
| 132. #494 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812141 | 2 |
| C2×#16812132 | 2 |
| C2×Q16×D107 | 2 |
| #20293202 | 2 |
| #20293020 | 2 |
| #20293019 | 2 |
| #20293012 | 2 |
| #20293011 | 2 |
| #20293005 | 2 |
| #20292581 | 2 |
| #494×C107 | 2 |
| #3156 | 107 |