Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20295035 | C2 | semidirect |
| 5. #20294787 | C2 | semidirect |
| 6. #20294785 | C2 | semidirect |
| 7. #419×C109 | C2 | semidirect |
| 11. #16812688 | C4 | semidirect |
| 42. C4×Dic109 | C2×C4 | semidirect |
| 48. C2×Q8×C109 | C2×C4 | semidirect |
| 108. C109 | #1885 | semidirect |
| 112. #419 | D109 | semidirect |
| 138. C2×Q8 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812688 | 2 |
| #20295500 | 2 |
| #20295035 | 2 |
| C2×#16812615 | 2 |
| #20294787 | 2 |
| #20294785 | 2 |
| #419×C109 | 2 |
| #1885 | 109 |