Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #20292379 | C2 | semidirect |
| 5. #20292378 | C2 | semidirect |
| 6. #20292377 | C2 | semidirect |
| 7. #335×C107 | C2 | semidirect |
| 56. C8×C107 | M16 | semidirect |
| 60. C107⋊C8 | M16 | semidirect |
| 78. C107 | #1569 | semidirect |
| 83. #335 | D107 | semidirect |
| 138. C8 | #13133801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292683 | 2 |
| #20292649 | 2 |
| C4×#13133801 | 2 |
| #20292379 | 2 |
| #20292378 | 2 |
| #20292377 | 2 |
| #335×C107 | 2 |
| #1569 | 107 |