Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #20295917 | C2 | semidirect |
| 4. #20295916 | C2 | semidirect |
| 9. #16812773 | C4 | semidirect |
| 10. D109⋊C16 | C4 | semidirect |
| 14. #16812638 | C4 | semidirect |
| 15. #16812638 | C4 | semidirect |
| 18. C2×#13182004 | C4 | semidirect |
| 19. C2×C16×C109 | C4 | semidirect |
| 65. C109 | #2110 | semidirect |
| 82. C2×C16 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊M32 | 2 |
| #20295989 | 2 |
| #20295917 | 2 |
| #20295916 | 2 |
| C2×#16812638 | 2 |
| #2110 | 109 |