Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #20294981 | C2 | semidirect |
| 5. #20294791 | C2 | semidirect |
| 6. #20294786 | C2 | semidirect |
| 7. C2×C4×C8×C109 | C2 | semidirect |
| 10. #16812705 | C4 | semidirect |
| 16. #16812627 | C4 | semidirect |
| 17. #16812624 | C4 | semidirect |
| 18. #16812621 | C4 | semidirect |
| 99. C109 | #1764 | semidirect |
| 104. C2×C4×C8 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812705 | 2 |
| C2×#16812627 | 2 |
| #20295023 | 2 |
| #20294981 | 2 |
| #20294791 | 2 |
| #20294786 | 2 |
| C2×C4×C8×C109 | 2 |
| #1764 | 109 |