Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 24. #13133808 | C8 | direct (N × H) |
| 53. C8×C107 | Q16 | semidirect |
| 72. C107 | C8×Q16 | semidirect |
| 129. C8 | #13133808 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic214 | 2 |
| C4×#13133808 | 2 |
| #20292379 | 2 |
| Q8⋊(C107⋊C8) | 2 |
| #20292357 | 2 |
| C8×C107⋊C8 | 2 |
| C8×Q8×C107 | 2 |
| C8×Q16 | 107 |