Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16812105 | C2 | semidirect |
| 3. C2×#16812036 | C2 | semidirect |
| 4. #20292631 | C2 | semidirect |
| 5. C2×#16812026 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #535×C107 | C2 | semidirect |
| 35. C2×D428 | D4 | semidirect |
| 44. #13133802 | D4 | semidirect |
| 48. C4×Dic107 | D4 | semidirect |
| 54. C2×Q8×C107 | D4 | semidirect |
| 63. C2×D4×C107 | D4 | semidirect |
| 66. C4⋊C4×C107 | D4 | semidirect |
| 139. C107 | #2002 | semidirect |
| 141. #535 | D107 | semidirect |
| 174. C2×Q8 | C22⋊D107 | semidirect |
| 191. C2×D4 | C22⋊D107 | semidirect |
| 203. C4⋊C4 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| C2×#16812105 | 2 |
| C2×#16812036 | 2 |
| #20292631 | 2 |
| C2×#16812026 | 2 |
| #20292386 | 2 |
| #535×C107 | 2 |
| #2002 | 107 |