Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 11. #16812107 | C4 | semidirect |
| 48. C4×Dic107 | Q8 | semidirect |
| 96. Dic107 | C4×Q8 | semidirect |
| 97. Dic107 | C4⋊Q8 | semidirect |
| 104. C107 | C4×C4⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812107 | 2 |
| C2×Q8×Dic107 | 2 |
| C2×#16812074 | 2 |
| #20292533 | 2 |
| #20292524 | 2 |
| #20292496 | 2 |
| #20292478 | 2 |
| C42×Dic107 | 2 |
| #391×C107 | 2 |
| C4×C4⋊Q8 | 107 |