Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. #20295576 | C2 | semidirect |
| 2. C2×C4×D436 | C2 | semidirect |
| 3. #20295345 | C2 | semidirect |
| 4. #20295317 | C2 | semidirect |
| 5. #20295222 | C2 | semidirect |
| 6. #20295162 | C2 | semidirect |
| 7. #20295139 | C2 | semidirect |
| 8. #432×C109 | C2 | semidirect |
| 13. #16812699 | C22 | semidirect |
| 14. #16812696 | C22 | semidirect |
| 23. C4×D436 | C22 | semidirect |
| 26. #16812631 | C22 | semidirect |
| 28. #16812621 | C22 | semidirect |
| 30. C4⋊C8×C109 | C22 | semidirect |
| 32. #97×C109 | C22 | semidirect |
| 89. D436 | #41 | semidirect |
| 121. C109 | #3109 | semidirect |
| 129. #432 | D109 | semidirect |
| 149. C4⋊C8 | C2×D109 | semidirect |
| 153. #97 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295576 | 2 |
| C2×C4×D436 | 2 |
| #20295345 | 2 |
| #20295317 | 2 |
| #20295222 | 2 |
| #20295162 | 2 |
| #20295139 | 2 |
| #432×C109 | 2 |
| #3109 | 109 |