Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #41×Dic109 | C2 | semidirect |
| 3. #20295042 | C2 | semidirect |
| 4. C2×#16812625 | C2 | semidirect |
| 5. #568×C109 | C2 | semidirect |
| 7. #16812746 | C4 | semidirect |
| 8. #16812745 | C4 | semidirect |
| 14. #16812658 | C22 | semidirect |
| 15. C2×C4×Dic109 | C22 | semidirect |
| 16. #16812625 | C22 | semidirect |
| 17. #16812625 | C22 | semidirect |
| 20. C2×M16×C109 | C22 | semidirect |
| 24. #13182029 | C2×C4 | semidirect |
| 27. C2×Dic218 | C2×C4 | semidirect |
| 29. C2×D436 | C2×C4 | semidirect |
| 84. C109 | #2901 | semidirect |
| 86. #568 | D109 | semidirect |
| 98. C2×M16 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295862 | 2 |
| #41×Dic109 | 2 |
| #20295042 | 2 |
| C2×#16812625 | 2 |
| #568×C109 | 2 |
| #2901 | 109 |