Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20293035 | C2 | semidirect |
| 4. #20293030 | C2 | semidirect |
| 5. #20293025 | C2 | semidirect |
| 6. #20293023 | C2 | semidirect |
| 9. #500×C107 | C2 | semidirect |
| 43. #13133801 | Q8 | semidirect |
| 86. C8×C107 | C2×Q8 | semidirect |
| 87. C107⋊C8 | C2×Q8 | semidirect |
| 107. C107 | #3165 | semidirect |
| 112. #500 | D107 | semidirect |
| 194. C8 | Q8×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293182 | 2 |
| C4⋊Q8×D107 | 2 |
| #20293035 | 2 |
| #20293030 | 2 |
| #20293025 | 2 |
| #20293023 | 2 |
| #20292668 | 2 |
| C4×#13133801 | 2 |
| #500×C107 | 2 |
| #3165 | 107 |