Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
224 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 3. #20292348 | C2 | semidirect |
| 4. C8×C107⋊C8 | C2 | semidirect |
| 24. M16×C107 | C8 | semidirect |
| 40. C8×C107 | C2×C8 | semidirect |
| 43. C107⋊C8 | M16 | direct (N × H) |
| 59. C107 | C8×M16 | semidirect |
| 79. M16 | C107⋊C8 | direct (N × H) |
| 102. C8 | C2×C107⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292680 | 2 |
| C2×C4×C107⋊C8 | 2 |
| #20292348 | 2 |
| C8×C107⋊C8 | 2 |
| C4×M16×C107 | 2 |
| C8×M16 | 107 |