Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×#16812606 | C2 | semidirect |
| 3. #20294764 | C2 | semidirect |
| 4. #20294761 | C2 | semidirect |
| 5. #407×C109 | C2 | semidirect |
| 6. C2×#13182029 | C4 | semidirect |
| 9. #16812678 | C4 | semidirect |
| 11. #16812673 | C4 | semidirect |
| 16. #16812658 | C4 | semidirect |
| 24. C2×Dic218 | C2×C4 | semidirect |
| 25. C2×D436 | C2×C4 | semidirect |
| 34. C4⋊Dic109 | C2×C4 | semidirect |
| 35. C4⋊Dic109 | C2×C4 | semidirect |
| 120. C109 | #1504 | semidirect |
| 122. #407 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295537 | 2 |
| C2×#16812606 | 2 |
| #20294764 | 2 |
| #20294761 | 2 |
| #407×C109 | 2 |
| #1504 | 109 |