Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×D856 | C2 | semidirect |
| 2. #20293062 | C2 | direct (N × H) |
| 3. C2×#16812052 | C2 | semidirect |
| 4. C2×#16812050 | C2 | semidirect |
| 5. C2×#16812049 | C2 | semidirect |
| 6. C2×#135×C107 | C2 | semidirect |
| 11. C2×D856 | C22 | semidirect |
| 12. #16812052 | C22 | semidirect |
| 13. #16812050 | C22 | semidirect |
| 14. #16812049 | C22 | semidirect |
| 15. C2×C107⋊C16 | C22 | semidirect |
| 18. #135×C107 | C22 | semidirect |
| 19. C2×Q16×C107 | C22 | semidirect |
| 21. C2×D8×C107 | C22 | semidirect |
| 31. C107⋊C16 | C23 | semidirect |
| 40. Q16×C107 | C23 | semidirect |
| 43. D8×C107 | C23 | semidirect |
| 84. C2×C107 | #509 | semidirect |
| 88. C107 | C2×#509 | semidirect |
| 89. C2×#135 | D107 | semidirect |
| 98. #135 | C2×D107 | semidirect |
| 99. C2×Q16 | C2×D107 | semidirect |
| 105. C2×D8 | C2×D107 | semidirect |
| 124. Q16 | C22×D107 | semidirect |
| 130. D8 | C22×D107 | semidirect |
| 173. C2 | #20293062 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D856 | 2 |
| #20293062 | 2 |
| C2×#16812052 | 2 |
| C2×#16812050 | 2 |
| C2×#16812049 | 2 |
| C2×#135×C107 | 2 |
| C2×#509 | 107 |