Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20292667 | C2 | semidirect |
| 4. #20292496 | C2 | semidirect |
| 5. #20292395 | C2 | semidirect |
| 6. #20292388 | C2 | semidirect |
| 20. #16812036 | C4 | semidirect |
| 30. #13133802 | C2×C4 | semidirect |
| 43. C4×Dic107 | C2×C4 | semidirect |
| 62. Q8×C107 | C4⋊C4 | semidirect |
| 66. D4×C107 | C4⋊C4 | semidirect |
| 113. C107 | #1859 | semidirect |
| 175. Q8 | Dic107⋊C4 | semidirect |
| 179. D4 | Dic107⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293110 | 2 |
| #20292667 | 2 |
| C2×#16812036 | 2 |
| #20292496 | 2 |
| #20292395 | 2 |
| #20292388 | 2 |
| #417×C107 | 2 |
| #1859 | 107 |