Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 70 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×#16812769 | C2 | semidirect |
| 2. C2×#16812764 | C2 | semidirect |
| 3. C2×#16812763 | C2 | semidirect |
| 4. #20296001 | C2 | semidirect |
| 5. #20296000 | C2 | semidirect |
| 6. C2×C8×#89137 | C2 | semidirect |
| 22. C2×#13182019 | C4 | semidirect |
| 23. C2×#13182018 | C4 | semidirect |
| 24. C2×#13182014 | C4 | semidirect |
| 26. C2×SD16×C109 | C4 | semidirect |
| 120. C109 | #1974 | semidirect |
| 134. C2×SD16 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812769 | 2 |
| C2×#16812764 | 2 |
| C2×#16812763 | 2 |
| #20296001 | 2 |
| #20296000 | 2 |
| C2×C8×#89137 | 2 |
| C2×#16812720 | 2 |
| #1974 | 109 |