Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 2. C22×Dic436 | C2 | semidirect |
| 3. C22×#13182017 | C2 | semidirect |
| 4. C2×#16812679 | C2 | semidirect |
| 5. #20295189 | C2 | direct (N × H) |
| 6. C2×#16812622 | C2 | semidirect |
| 7. C2×#16812611 | C2 | semidirect |
| 8. C2×#102×C109 | C2 | semidirect |
| 19. C2×Dic436 | C22 | semidirect |
| 21. C2×#13182017 | C22 | semidirect |
| 24. #16812679 | C22 | semidirect |
| 27. #16812622 | C22 | semidirect |
| 28. #16812611 | C22 | semidirect |
| 32. #102×C109 | C22 | semidirect |
| 130. C2×C109 | #452 | semidirect |
| 136. C109 | C2×#452 | semidirect |
| 143. C2×#102 | D109 | semidirect |
| 167. #102 | C2×D109 | semidirect |
| 267. C2 | #20295189 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182028 | 2 |
| C22×Dic436 | 2 |
| C22×#13182017 | 2 |
| C2×#16812679 | 2 |
| #20295189 | 2 |
| C2×#16812622 | 2 |
| C2×#16812611 | 2 |
| C2×#102×C109 | 2 |
| C2×#452 | 109 |