Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #20292454 | C2 | semidirect |
| 4. #20292431 | C2 | semidirect |
| 6. C4×C107⋊C16 | C2 | semidirect |
| 7. C4×Q16×C107 | C2 | semidirect |
| 10. #16812052 | C4 | direct (N × H) |
| 27. C107⋊C16 | C2×C4 | semidirect |
| 30. Q16×C107 | C2×C4 | semidirect |
| 59. C4×C107 | SD32 | semidirect |
| 68. C107 | C4×SD32 | semidirect |
| 70. C4×Q16 | D107 | semidirect |
| 92. Q16 | C4×D107 | semidirect |
| 128. C4 | #16812052 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812052 | 2 |
| C4×D856 | 2 |
| #20292454 | 2 |
| #20292431 | 2 |
| #20292427 | 2 |
| C4×C107⋊C16 | 2 |
| C4×Q16×C107 | 2 |
| C4×SD32 | 107 |