Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20295049 | C2 | semidirect |
| 3. C2×#16812627 | C2 | semidirect |
| 4. C2×#16812626 | C2 | semidirect |
| 5. C2×#16812625 | C2 | semidirect |
| 6. C42×Dic109 | C2 | semidirect |
| 7. C2×#104×C109 | C2 | semidirect |
| 10. #16812697 | C4 | semidirect |
| 11. #16812695 | C4 | semidirect |
| 12. #16812688 | C4 | semidirect |
| 13. #16812686 | C4 | semidirect |
| 49. C4×Dic109 | D4 | semidirect |
| 64. C42×C109 | D4 | semidirect |
| 119. Dic109 | #104 | semidirect |
| 127. C109 | #1962 | semidirect |
| 133. C2×#104 | D109 | semidirect |
| 191. C42 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295572 | 2 |
| #20295049 | 2 |
| C2×#16812627 | 2 |
| C2×#16812626 | 2 |
| C2×#16812625 | 2 |
| C42×Dic109 | 2 |
| C2×#104×C109 | 2 |
| #1962 | 109 |