Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. M16×Dic107 | C2 | semidirect |
| 5. C42×Dic107 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #339×C107 | C2 | semidirect |
| 10. #16812074 | C4 | semidirect |
| 11. #16812071 | C4 | semidirect |
| 18. #16812037 | C4 | semidirect |
| 19. #16812035 | C4 | semidirect |
| 37. #13133802 | C2×C4 | semidirect |
| 45. C4×Dic107 | C2×C4 | semidirect |
| 51. M16×C107 | C2×C4 | semidirect |
| 57. C42×C107 | C2×C4 | semidirect |
| 78. D428 | C42 | semidirect |
| 83. Dic214 | C42 | semidirect |
| 101. Dic107 | #104 | semidirect |
| 108. C107 | C4×#104 | semidirect |
| 115. #339 | D107 | semidirect |
| 149. M16 | C4×D107 | semidirect |
| 165. C42 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293095 | 2 |
| C2×#16812037 | 2 |
| C2×#16812035 | 2 |
| M16×Dic107 | 2 |
| C42×Dic107 | 2 |
| #20292386 | 2 |
| #339×C107 | 2 |
| C4×#104 | 107 |