Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊(C107⋊C8) | C2 | semidirect |
| 3. C2×#16812029 | C2 | semidirect |
| 4. C4×C4⋊C4×C107 | C2 | semidirect |
| 10. #16812106 | C4 | semidirect |
| 34. C4⋊C4×C107 | D4 | semidirect |
| 74. C4×C107 | #102 | semidirect |
| 85. C107 | #1982 | semidirect |
| 89. C4×C4⋊C4 | D107 | semidirect |
| 119. C4⋊C4 | D428 | semidirect |
| 159. C4 | #16812029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812106 | 2 |
| C2×C4⋊(C107⋊C8) | 2 |
| C2×#16812029 | 2 |
| C4×C4⋊C4×C107 | 2 |
| #1982 | 107 |