Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
224 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×C16×D107 | C2 | semidirect |
| 3. #108×D107 | C2 | semidirect |
| 4. #20292435 | C2 | semidirect |
| 5. #20292434 | C2 | semidirect |
| 6. #20292433 | C2 | semidirect |
| 7. #359×C107 | C2 | semidirect |
| 19. C2×C107⋊C16 | C22 | semidirect |
| 22. #16812045 | C22 | semidirect |
| 25. C2×C16×C107 | C22 | semidirect |
| 26. #108×C107 | C22 | semidirect |
| 107. D107 | #359 | direct (N × H) |
| 109. C107 | C2×#359 | semidirect |
| 116. #359 | D107 | direct (N × H) |
| 132. C2×C16 | C2×D107 | semidirect |
| 135. #108 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D107 | 2 |
| C2×C16×D107 | 2 |
| #108×D107 | 2 |
| #20292435 | 2 |
| #20292434 | 2 |
| #20292433 | 2 |
| #359×C107 | 2 |
| C2×#359 | 107 |