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×#13182016 | C2 | semidirect |
| 3. C2×#16812675 | C2 | semidirect |
| 4. #20295187 | C2 | direct (N × H) |
| 5. C2×#16812623 | C2 | semidirect |
| 6. C2×#16812621 | C2 | semidirect |
| 7. C2×#16812611 | C2 | semidirect |
| 8. C22×Q16×C109 | C2 | semidirect |
| 18. C2×#13182016 | C22 | semidirect |
| 21. #16812675 | C22 | semidirect |
| 25. #16812623 | C22 | semidirect |
| 26. #16812621 | C22 | semidirect |
| 27. #16812611 | C22 | semidirect |
| 31. C2×Q16×C109 | C22 | semidirect |
| 129. C2×C109 | #452 | semidirect |
| 136. C109 | C2×#452 | semidirect |
| 138. C22×Q16 | D109 | semidirect |
| 156. C2×Q16 | C2×D109 | semidirect |
| 267. C2 | #20295187 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182030 | 2 |
| C22×#13182016 | 2 |
| C2×#16812675 | 2 |
| #20295187 | 2 |
| C2×#16812623 | 2 |
| C2×#16812621 | 2 |
| C2×#16812611 | 2 |
| C22×Q16×C109 | 2 |
| C2×#452 | 109 |