Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
182 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 182 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 |
|---|---|---|
| 1. #20292705 | C2 | semidirect |
| 2. D4×C107⋊C8 | C2 | semidirect |
| 3. #20292378 | C2 | semidirect |
| 4. D4⋊(C107⋊C8) | C2 | semidirect |
| 5. D4⋊(C107⋊C8) | C2 | semidirect |
| 6. #20292349 | C2 | semidirect |
| 47. D4×C107 | M16 | semidirect |
| 84. C107 | #1586 | semidirect |
| 131. D4 | #13133802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292705 | 2 |
| D4×C107⋊C8 | 2 |
| #20292378 | 2 |
| D4⋊(C107⋊C8) | 2 |
| #20292349 | 2 |
| C4×D8×C107 | 2 |
| #1586 | 107 |