Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 211 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. #20293045 | C2 | semidirect |
| 3. #20293044 | C2 | semidirect |
| 4. #20293043 | C2 | semidirect |
| 5. M32×D107 | C2 | semidirect |
| 6. C2×C16×D107 | C2 | semidirect |
| 7. #504×C107 | C2 | semidirect |
| 14. #16812049 | C22 | semidirect |
| 15. #16812048 | C22 | semidirect |
| 16. C2×C107⋊C16 | C22 | semidirect |
| 19. C16×D107 | C22 | semidirect |
| 20. C16×D107 | C22 | semidirect |
| 22. M32×C107 | C22 | semidirect |
| 23. C2×C16×C107 | C22 | semidirect |
| 71. D107 | #504 | direct (N × H) |
| 73. C107 | C2×#504 | semidirect |
| 78. #504 | D107 | direct (N × H) |
| 90. M32 | C2×D107 | semidirect |
| 96. C2×C16 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D107 | 2 |
| #20293045 | 2 |
| #20293044 | 2 |
| #20293043 | 2 |
| M32×D107 | 2 |
| C2×C16×D107 | 2 |
| #504×C107 | 2 |
| C2×#504 | 107 |