Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×#16812658 | C2 | semidirect |
| 3. #20294966 | C2 | semidirect |
| 4. #20294963 | C2 | semidirect |
| 5. #20294958 | C2 | semidirect |
| 6. #20294953 | C2 | semidirect |
| 7. #20294951 | C2 | semidirect |
| 9. C4×C4⋊Dic109 | C2 | semidirect |
| 10. C4×#13182006 | C2 | semidirect |
| 11. C4×C22⋊C4×C109 | C2 | semidirect |
| 138. C109 | #2395 | semidirect |
| 149. C4×C22⋊C4 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D109 | 2 |
| C2×#16812658 | 2 |
| #20294966 | 2 |
| #20294963 | 2 |
| #20294958 | 2 |
| #20294953 | 2 |
| #20294951 | 2 |
| #20294942 | 2 |
| C4×C4⋊Dic109 | 2 |
| C4×#13182006 | 2 |
| C4×C22⋊C4×C109 | 2 |
| #2395 | 109 |