Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20292754 | C2 | semidirect |
| 4. #20292357 | C2 | semidirect |
| 6. #20292349 | C2 | semidirect |
| 7. #334×C107 | C2 | semidirect |
| 60. C107⋊C8 | SD16 | semidirect |
| 78. C107 | #1582 | semidirect |
| 82. #334 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292754 | 2 |
| C4×#13133807 | 2 |
| #20292692 | 2 |
| #20292357 | 2 |
| #20292354 | 2 |
| #20292349 | 2 |
| #334×C107 | 2 |
| #1582 | 107 |