Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic107 | C2 | semidirect |
| 3. C2×#16812035 | C2 | semidirect |
| 4. #20292600 | C2 | semidirect |
| 5. #20292398 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #421×C107 | C2 | semidirect |
| 10. #16812139 | C4 | semidirect |
| 12. #16812134 | C4 | semidirect |
| 33. C2×Dic214 | C2×C4 | semidirect |
| 34. C2×D428 | C2×C4 | semidirect |
| 44. #13133802 | C2×C4 | semidirect |
| 130. C107 | #1906 | semidirect |
| 133. #421 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293425 | 2 |
| #41×Dic107 | 2 |
| C2×#16812035 | 2 |
| #20292600 | 2 |
| #20292398 | 2 |
| #20292386 | 2 |
| #421×C107 | 2 |
| #1906 | 107 |