Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#13133803 | C2 | semidirect |
| 2. C2×#16812030 | C2 | semidirect |
| 3. #20292529 | C2 | semidirect |
| 4. #20292382 | C2 | semidirect |
| 5. C2×#127×C107 | C2 | semidirect |
| 22. C2×D428 | D4 | semidirect |
| 27. C2×C107⋊C8 | D4 | semidirect |
| 61. C2×C4×C107 | D8 | semidirect |
| 98. C107 | #2011 | semidirect |
| 100. C2×#127 | D107 | semidirect |
| 163. C2×C4 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133803 | 2 |
| C2×#16812030 | 2 |
| #20292529 | 2 |
| #20292382 | 2 |
| C2×#127×C107 | 2 |
| #2011 | 107 |