Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #20293035 | C2 | semidirect |
| 3. #20293033 | C2 | semidirect |
| 4. #20293031 | C2 | semidirect |
| 5. #20293029 | C2 | semidirect |
| 6. #20293028 | C2 | semidirect |
| 11. #500×C107 | C2 | semidirect |
| 42. #13133801 | Q8 | semidirect |
| 45. C8×D107 | Q8 | semidirect |
| 108. C107 | #3164 | semidirect |
| 113. #500 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293254 | 2 |
| #20293035 | 2 |
| #20293033 | 2 |
| #20293031 | 2 |
| #20293029 | 2 |
| #20293028 | 2 |
| #20292668 | 2 |
| #20292664 | 2 |
| #107×D107 | 2 |
| #20292581 | 2 |
| #500×C107 | 2 |
| #3164 | 107 |