Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C2×#16812101 | C2 | semidirect |
| 2. #20292927 | C2 | direct (N × H) |
| 3. C2×#16812042 | C2 | semidirect |
| 4. C2×#16812040 | C2 | semidirect |
| 5. C2×C4⋊(C107⋊C8) | C2 | semidirect |
| 12. #16812101 | C22 | semidirect |
| 17. #16812042 | C22 | semidirect |
| 18. #16812040 | C22 | semidirect |
| 19. C4⋊(C107⋊C8) | C22 | semidirect |
| 99. C2×C107 | #478 | semidirect |
| 104. C107 | C2×#478 | semidirect |
| 203. C2 | #20292927 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812101 | 2 |
| #20292927 | 2 |
| C2×#16812042 | 2 |
| C2×#16812040 | 2 |
| C2×C4⋊(C107⋊C8) | 2 |
| C2×#16812030 | 2 |
| C2×C4×D4×C107 | 2 |
| C2×#478 | 107 |