Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
652 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 209 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×#16812074 | C2 | semidirect |
| 4. #20292532 | C2 | semidirect |
| 6. #20292516 | C2 | semidirect |
| 7. #20292474 | C2 | semidirect |
| 8. C42×Dic107 | C2 | semidirect |
| 9. #382×C107 | C2 | semidirect |
| 13. #16812097 | C4 | semidirect |
| 33. C2×Dic214 | C2×C4 | semidirect |
| 46. (C2×D107)⋊C4 | C2×C4 | semidirect |
| 58. C42×C107 | C2×C4 | semidirect |
| 105. Dic107 | #124 | semidirect |
| 113. C107 | C4×#124 | semidirect |
| 120. #382 | D107 | semidirect |
| 171. C42 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812097 | 2 |
| C2×#16812074 | 2 |
| C2×#16812071 | 2 |
| #20292532 | 2 |
| #20292528 | 2 |
| #20292516 | 2 |
| #20292474 | 2 |
| C42×Dic107 | 2 |
| #382×C107 | 2 |
| C4×#124 | 107 |