Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q16×Dic107 | C2 | semidirect |
| 4. #20292454 | C2 | semidirect |
| 6. C16×Dic107 | C2 | semidirect |
| 7. #358×C107 | C2 | semidirect |
| 11. #16812052 | C4 | semidirect |
| 30. C107⋊C16 | C2×C4 | semidirect |
| 33. Q16×C107 | C2×C4 | semidirect |
| 62. Dic107 | SD32 | semidirect |
| 68. C107 | C4×SD32 | semidirect |
| 73. #358 | D107 | semidirect |
| 92. Q16 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812052 | 2 |
| Q16×Dic107 | 2 |
| #20292709 | 2 |
| #20292454 | 2 |
| #20292429 | 2 |
| C16×Dic107 | 2 |
| #358×C107 | 2 |
| C4×SD32 | 107 |