Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
416 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20292922 | C2 | direct (N × H) |
| 33. C2×Q8×C107 | Q8 | semidirect |
| 49. Q8×C107 | C2×Q8 | semidirect |
| 78. C2×C107 | #477 | semidirect |
| 83. C107 | C2×#477 | semidirect |
| 110. C2×Q8 | Dic214 | semidirect |
| 133. Q8 | C2×Dic214 | semidirect |
| 161. C2 | #20292922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812109 | 2 |
| #20292922 | 2 |
| C2×#16812042 | 2 |
| C2×C4⋊(C107⋊C8) | 2 |
| C2×#16812033 | 2 |
| C2×C4×Q8×C107 | 2 |
| C2×#477 | 107 |