Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×Q8×Dic107 | C2 | semidirect |
| 5. #20292519 | C2 | semidirect |
| 6. #20292492 | C2 | semidirect |
| 7. #20292474 | C2 | semidirect |
| 8. C42×Dic107 | C2 | semidirect |
| 9. #391×C107 | C2 | semidirect |
| 12. #16812098 | C4 | semidirect |
| 44. (C2×D107)⋊C4 | C2×C4 | semidirect |
| 48. C4×Dic107 | C2×C4 | semidirect |
| 52. C2×Q8×C107 | C2×C4 | semidirect |
| 105. Dic107 | #124 | semidirect |
| 113. C107 | C4×#124 | semidirect |
| 117. #391 | D107 | semidirect |
| 146. C2×Q8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812098 | 2 |
| C2×Q8×Dic107 | 2 |
| C2×#16812071 | 2 |
| #20292529 | 2 |
| #20292519 | 2 |
| #20292492 | 2 |
| #20292474 | 2 |
| C42×Dic107 | 2 |
| #391×C107 | 2 |
| C4×#124 | 107 |