Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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×#16812627 | C2 | semidirect |
| 3. C2×#16812626 | C2 | semidirect |
| 4. C2×#16812625 | C2 | semidirect |
| 5. M16×Dic109 | C2 | semidirect |
| 6. C4×#13182008 | C2 | semidirect |
| 7. C2×#104×C109 | C2 | semidirect |
| 10. #16812697 | C4 | semidirect |
| 11. #16812695 | C4 | semidirect |
| 12. #16812688 | C4 | semidirect |
| 13. #16812686 | C4 | semidirect |
| 45. #13182013 | D4 | semidirect |
| 71. M16×C109 | D4 | semidirect |
| 140. Dic109 | #104 | semidirect |
| 149. C109 | #1980 | semidirect |
| 154. C2×#104 | D109 | semidirect |
| 206. M16 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295572 | 2 |
| C2×#16812627 | 2 |
| C2×#16812626 | 2 |
| C2×#16812625 | 2 |
| M16×Dic109 | 2 |
| C4×#13182008 | 2 |
| C2×#104×C109 | 2 |
| #1980 | 109 |