Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20293258 | C2 | semidirect |
| 3. #20292936 | C2 | semidirect |
| 4. #20292925 | C2 | semidirect |
| 5. #20292915 | C2 | semidirect |
| 6. #20292910 | C2 | semidirect |
| 7. #20292669 | C2 | semidirect |
| 8. C2×#16812040 | C2 | semidirect |
| 9. #20292655 | C2 | semidirect |
| 64. #41×C107 | Q8 | semidirect |
| 124. C107 | #3084 | semidirect |
| 166. #41 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293258 | 2 |
| #20293110 | 2 |
| #20292936 | 2 |
| #20292925 | 2 |
| #20292915 | 2 |
| #20292910 | 2 |
| #20292669 | 2 |
| C2×#16812040 | 2 |
| #20292655 | 2 |
| #20292623 | 2 |
| #417×C107 | 2 |
| #3084 | 107 |