Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
448 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 138 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. #20295899 | C2 | semidirect |
| 7. D109⋊M16 | C4 | semidirect |
| 11. #16812778 | C4 | semidirect |
| 17. C2×C4⋊Dic109 | C4 | semidirect |
| 21. C4⋊C4×D109 | C4 | semidirect |
| 23. C2×C4⋊C4×C109 | C4 | semidirect |
| 28. D109⋊C8 | C2×C4 | semidirect |
| 31. C4⋊#89137 | C2×C4 | semidirect |
| 121. C109 | #1736 | semidirect |
| 142. C2×C4⋊C4 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D109⋊M16 | 2 |
| C2×#16812778 | 2 |
| #20295899 | 2 |
| C2×C4⋊C4×D109 | 2 |
| #1736 | 109 |