Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#16812140 | C2 | semidirect |
| 3. C2×#16812098 | C2 | semidirect |
| 4. C2×#16812035 | C2 | semidirect |
| 5. C2×#16812025 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #419×C107 | C2 | semidirect |
| 49. #13133802 | D4 | semidirect |
| 54. C4×Dic107 | D4 | semidirect |
| 60. C2×Q8×C107 | D4 | semidirect |
| 132. C107 | #2004 | semidirect |
| 137. #419 | D107 | semidirect |
| 172. C2×Q8 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812140 | 2 |
| #20293196 | 2 |
| C2×#16812098 | 2 |
| C2×#16812035 | 2 |
| C2×#16812025 | 2 |
| #20292386 | 2 |
| #419×C107 | 2 |
| #2004 | 107 |