Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #20295792 | C2 | semidirect |
| 3. #20295149 | C2 | semidirect |
| 4. #20295144 | C2 | semidirect |
| 5. #20295075 | C2 | semidirect |
| 6. C2×#16812627 | C2 | semidirect |
| 7. C4×M16×C109 | C2 | semidirect |
| 9. #16812732 | C4 | semidirect |
| 10. #16812727 | C4 | semidirect |
| 13. #16812705 | C22 | semidirect |
| 16. #16812635 | C22 | semidirect |
| 17. #16812627 | C22 | semidirect |
| 18. #16812627 | C22 | semidirect |
| 22. #97×C109 | C22 | semidirect |
| 23. C4×C8×C109 | C22 | semidirect |
| 32. Dic436 | C2×C4 | semidirect |
| 33. #13182018 | C2×C4 | semidirect |
| 34. D872 | C2×C4 | semidirect |
| 86. C109 | #2956 | semidirect |
| 93. C4×M16 | D109 | semidirect |
| 108. #97 | C2×D109 | semidirect |
| 109. C4×C8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295826 | 2 |
| #20295792 | 2 |
| #20295149 | 2 |
| #20295144 | 2 |
| #20295075 | 2 |
| C2×#16812627 | 2 |
| C4×M16×C109 | 2 |
| #2956 | 109 |