Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #20293109 | C2 | semidirect |
| 3. #20292740 | C2 | semidirect |
| 4. #20292738 | C2 | semidirect |
| 5. #20292734 | C2 | semidirect |
| 6. C4×#13133805 | C2 | semidirect |
| 7. #20292712 | C2 | semidirect |
| 8. #106×D107 | C2 | semidirect |
| 9. #20292627 | C2 | semidirect |
| 10. #20292584 | C2 | semidirect |
| 11. #441×C107 | C2 | semidirect |
| 13. #16812132 | C4 | semidirect |
| 41. #13133819 | C2×C4 | semidirect |
| 49. #13133805 | C2×C4 | semidirect |
| 50. D856 | C2×C4 | semidirect |
| 54. C8×D107 | C2×C4 | semidirect |
| 65. Q16×C107 | C2×C4 | semidirect |
| 115. C107 | #2952 | semidirect |
| 121. #441 | D107 | semidirect |
| 165. Q16 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| #20293109 | 2 |
| #20292740 | 2 |
| #20292738 | 2 |
| #20292734 | 2 |
| C4×#13133805 | 2 |
| #20292712 | 2 |
| #106×D107 | 2 |
| #20292627 | 2 |
| #20292584 | 2 |
| #441×C107 | 2 |
| #2952 | 107 |