Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16812129 | C2 | semidirect |
| 2. #20293177 | C2 | semidirect |
| 3. #20293009 | C2 | semidirect |
| 4. #20293006 | C2 | semidirect |
| 5. #20293003 | C2 | semidirect |
| 6. #20293001 | C2 | semidirect |
| 7. #20292999 | C2 | semidirect |
| 8. C2×C4×C107⋊C8 | C2 | semidirect |
| 9. #532×C107 | C2 | semidirect |
| 42. C2×C107⋊C8 | D4 | semidirect |
| 93. C4×C107 | #135 | semidirect |
| 102. C107 | #3147 | semidirect |
| 105. #532 | D107 | semidirect |
| 196. C4 | #16812129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812129 | 2 |
| #20293177 | 2 |
| #20293009 | 2 |
| #20293006 | 2 |
| #20293003 | 2 |
| #20293001 | 2 |
| #20292999 | 2 |
| C2×C4×C107⋊C8 | 2 |
| #532×C107 | 2 |
| #3147 | 107 |