Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16812042 | C2 | semidirect |
| 4. #20292525 | C2 | semidirect |
| 5. #20292389 | C2 | semidirect |
| 6. #20292382 | C2 | semidirect |
| 15. #16812030 | C4 | semidirect |
| 31. C2×C107⋊C8 | C2×C4 | semidirect |
| 35. C4⋊Dic107 | C2×C4 | semidirect |
| 67. D4×C107 | C4⋊C4 | semidirect |
| 124. C107 | #1862 | semidirect |
| 191. D4 | Dic107⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812042 | 2 |
| C2×#16812030 | 2 |
| #20292525 | 2 |
| #20292389 | 2 |
| #20292382 | 2 |
| C2×C4×D4×C107 | 2 |
| #1862 | 107 |