Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16812621 | C2 | semidirect |
| 3. #20294886 | C2 | semidirect |
| 4. #20294789 | C2 | semidirect |
| 5. C22×M16×C109 | C2 | semidirect |
| 9. #16812673 | C4 | semidirect |
| 45. C2×C8×C109 | D4 | semidirect |
| 105. C109 | #1895 | semidirect |
| 106. C22×M16 | D109 | semidirect |
| 144. C2×C8 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812673 | 2 |
| C2×#16812621 | 2 |
| #20294886 | 2 |
| #20294789 | 2 |
| C22×M16×C109 | 2 |
| #1895 | 109 |