Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20293178 | C2 | semidirect |
| 2. C4×#13133819 | C2 | semidirect |
| 3. #20292953 | C2 | semidirect |
| 4. #20292904 | C2 | semidirect |
| 5. #20292827 | C2 | semidirect |
| 6. #20292823 | C2 | semidirect |
| 7. #20292775 | C2 | semidirect |
| 8. #20292738 | C2 | semidirect |
| 9. #20292730 | C2 | semidirect |
| 10. #20292683 | C2 | semidirect |
| 11. #475×C107 | C2 | semidirect |
| 88. Q8×C107 | #41 | semidirect |
| 106. D428 | #41 | semidirect |
| 145. C107 | #3115 | semidirect |
| 149. #475 | D107 | semidirect |
| 233. Q8 | #13133819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293178 | 2 |
| C4×#13133819 | 2 |
| #20292953 | 2 |
| #20292904 | 2 |
| #20292827 | 2 |
| #20292823 | 2 |
| #20292775 | 2 |
| #20292738 | 2 |
| #20292730 | 2 |
| #20292683 | 2 |
| #475×C107 | 2 |
| #3115 | 107 |