Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 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 |
|---|---|---|
| 2. #20292705 | C2 | semidirect |
| 3. #20292692 | C2 | semidirect |
| 4. #20292379 | C2 | semidirect |
| 5. #20292356 | C2 | semidirect |
| 6. #20292349 | C2 | semidirect |
| 7. D4⋊C8×C107 | C2 | semidirect |
| 54. D428 | M16 | semidirect |
| 63. C107⋊C8 | D8 | semidirect |
| 84. C107 | #1581 | semidirect |
| 90. D4⋊C8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133803 | 2 |
| #20292705 | 2 |
| #20292692 | 2 |
| #20292379 | 2 |
| #20292356 | 2 |
| #20292349 | 2 |
| D4⋊C8×C107 | 2 |
| #1581 | 107 |