Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#16812117 | C2 | semidirect |
| 2. C22×#13133801 | C2 | semidirect |
| 4. #20292704 | C2 | semidirect |
| 5. #20292697 | C2 | semidirect |
| 6. #20292593 | C2 | semidirect |
| 7. #20292590 | C2 | semidirect |
| 8. #20292583 | C2 | semidirect |
| 9. #424×C107 | C2 | semidirect |
| 17. C2×#13133801 | C22 | semidirect |
| 19. C2×C8×D107 | C22 | semidirect |
| 26. (C2×D107)⋊C8 | C22 | semidirect |
| 27. #16812020 | C22 | semidirect |
| 28. C4×C107⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C107 | C22 | semidirect |
| 50. C2×C107⋊C8 | D4 | semidirect |
| 114. C107 | #2930 | semidirect |
| 120. #424 | D107 | semidirect |
| 142. C4⋊C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812117 | 2 |
| C22×#13133801 | 2 |
| #20293139 | 2 |
| #20292704 | 2 |
| #20292697 | 2 |
| #20292593 | 2 |
| #20292590 | 2 |
| #20292583 | 2 |
| #424×C107 | 2 |
| #2930 | 107 |