Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20293107 | C2 | semidirect |
| 3. C2×#16812035 | C2 | semidirect |
| 4. #20292530 | C2 | semidirect |
| 5. #20292395 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #418×C107 | C2 | semidirect |
| 10. #16812135 | C4 | semidirect |
| 42. #13133802 | C2×C4 | semidirect |
| 58. C2×D4×C107 | C2×C4 | semidirect |
| 95. D428 | C22⋊C4 | semidirect |
| 100. Dic214 | C22⋊C4 | semidirect |
| 133. C107 | #1883 | semidirect |
| 137. #418 | D107 | semidirect |
| 174. C2×D4 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812135 | 2 |
| #20293107 | 2 |
| C2×#16812035 | 2 |
| #20292530 | 2 |
| #20292395 | 2 |
| #20292386 | 2 |
| #418×C107 | 2 |
| #1883 | 107 |