Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16812134 | C2 | semidirect |
| 2. C2×#16812098 | C2 | semidirect |
| 3. #20292800 | C2 | direct (N × H) |
| 4. C2×#16812036 | C2 | semidirect |
| 5. C2×#16812028 | C2 | semidirect |
| 6. C2×2−1+4×C107 | C2 | semidirect |
| 9. #16812134 | C22 | semidirect |
| 14. #16812098 | C22 | semidirect |
| 17. #16812036 | C22 | semidirect |
| 18. #16812028 | C22 | semidirect |
| 21. 2−1+4×C107 | C22 | semidirect |
| 114. C2×C107 | #454 | semidirect |
| 118. C107 | C2×#454 | semidirect |
| 119. C2×2−1+4 | D107 | semidirect |
| 127. 2−1+4 | C2×D107 | semidirect |
| 233. C2 | #20292800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| C2×#16812098 | 2 |
| #20292800 | 2 |
| C2×#16812036 | 2 |
| C2×#16812028 | 2 |
| C2×2−1+4×C107 | 2 |
| C2×#454 | 107 |