Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C4⋊Q8×D107 | C2 | semidirect |
| 3. #20292920 | C2 | semidirect |
| 4. #20292916 | C2 | semidirect |
| 5. #20292912 | C2 | semidirect |
| 6. #20292908 | C2 | semidirect |
| 7. #20292904 | C2 | semidirect |
| 8. #20292666 | C2 | semidirect |
| 9. #20292649 | C2 | semidirect |
| 11. #475×C107 | C2 | semidirect |
| 44. #13133819 | Q8 | semidirect |
| 86. Q8×C107 | C2×Q8 | semidirect |
| 100. D428 | C2×Q8 | semidirect |
| 138. C107 | #3079 | semidirect |
| 144. #475 | D107 | semidirect |
| 226. Q8 | Q8×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D107 | 2 |
| C4×#13133819 | 2 |
| #20292920 | 2 |
| #20292916 | 2 |
| #20292912 | 2 |
| #20292908 | 2 |
| #20292904 | 2 |
| #20292666 | 2 |
| #20292649 | 2 |
| #20292627 | 2 |
| #475×C107 | 2 |
| #3079 | 107 |