Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20293334 | C2 | semidirect |
| 2. #20292999 | C2 | semidirect |
| 3. #20292824 | C2 | semidirect |
| 4. #20292375 | C2 | semidirect |
| 5. #20292357 | C2 | semidirect |
| 6. D4⋊(C107⋊C8) | C2 | semidirect |
| 58. D4×C107 | SD16 | semidirect |
| 97. C107 | #1622 | semidirect |
| 158. D4 | #13133806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293334 | 2 |
| #20292999 | 2 |
| #20292824 | 2 |
| #20292375 | 2 |
| #20292357 | 2 |
| D4⋊(C107⋊C8) | 2 |
| #459×C107 | 2 |
| #1622 | 107 |