Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20292683 | C2 | semidirect |
| 3. C4×#13133801 | C2 | semidirect |
| 4. #20292356 | C2 | semidirect |
| 5. D4⋊(C107⋊C8) | C2 | semidirect |
| 6. #20292354 | C2 | semidirect |
| 7. D4⋊C8×C107 | C2 | semidirect |
| 19. C4⋊(C107⋊C8) | C22 | semidirect |
| 23. C4×C107⋊C8 | C22 | semidirect |
| 25. C4⋊C8×C107 | C22 | semidirect |
| 26. C4×C8×C107 | C22 | semidirect |
| 66. D4×C107 | M16 | semidirect |
| 80. D428 | M16 | semidirect |
| 122. C107 | #1490 | semidirect |
| 129. D4⋊C8 | D107 | semidirect |
| 143. C4⋊C8 | C2×D107 | semidirect |
| 148. C4×C8 | C2×D107 | semidirect |
| 191. D4 | #13133801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D107 | 2 |
| #20292683 | 2 |
| C4×#13133801 | 2 |
| #20292356 | 2 |
| D4⋊(C107⋊C8) | 2 |
| #20292354 | 2 |
| D4⋊C8×C107 | 2 |
| #1490 | 107 |