Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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×#13182013 | C2 | semidirect |
| 3. C2×#16812627 | C2 | direct (N × H) |
| 4. C22×C42×C109 | C2 | semidirect |
| 7. C2×#13182029 | C4 | semidirect |
| 9. C22×Dic218 | C4 | semidirect |
| 10. C22×D436 | C4 | semidirect |
| 14. C2×#13182013 | C22 | semidirect |
| 16. #16812627 | C22 | direct (N × H) |
| 20. C2×C42×C109 | C22 | semidirect |
| 25. #13182029 | C2×C4 | semidirect |
| 28. C2×Dic218 | C2×C4 | semidirect |
| 30. C2×D436 | C2×C4 | semidirect |
| 37. #13182013 | C23 | semidirect |
| 49. C42×C109 | C23 | semidirect |
| 71. D436 | C22×C4 | semidirect |
| 75. Dic218 | C22×C4 | semidirect |
| 79. C22×C109 | #104 | semidirect |
| 93. C2×C109 | C2×#104 | semidirect |
| 97. C109 | C22×#104 | semidirect |
| 100. C22×C42 | D109 | semidirect |
| 116. C2×C42 | C2×D109 | semidirect |
| 146. C42 | C22×D109 | semidirect |
| 178. C22 | #16812627 | direct (N × H) |
| 191. C2 | C2×#16812627 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182029 | 2 |
| C22×#13182013 | 2 |
| C2×#16812627 | 2 |
| C22×C42×C109 | 2 |
| C22×#104 | 109 |