Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#16812664 | C2 | semidirect |
| 4. #20294931 | C2 | semidirect |
| 6. #20294916 | C2 | semidirect |
| 7. #20294897 | C2 | semidirect |
| 8. #20294872 | C2 | semidirect |
| 9. #384×C109 | C2 | semidirect |
| 13. #16812687 | C4 | semidirect |
| 33. C2×Dic218 | C2×C4 | semidirect |
| 46. #13182006 | C2×C4 | semidirect |
| 57. C42×C109 | C2×C4 | semidirect |
| 112. C109 | #2326 | semidirect |
| 120. #384 | D109 | semidirect |
| 169. C42 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812687 | 2 |
| C2×#16812664 | 2 |
| C2×#16812661 | 2 |
| #20294931 | 2 |
| #20294927 | 2 |
| #20294916 | 2 |
| #20294897 | 2 |
| #20294872 | 2 |
| #384×C109 | 2 |
| #2326 | 109 |