Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#16812656 | C2 | semidirect |
| 3. C2×C4⋊C4×D109 | C2 | semidirect |
| 4. #20294932 | C2 | semidirect |
| 5. #20294931 | C2 | semidirect |
| 6. #20294929 | C2 | semidirect |
| 7. #20294902 | C2 | semidirect |
| 8. #20294884 | C2 | semidirect |
| 9. #390×C109 | C2 | semidirect |
| 12. C2×#13182028 | C4 | semidirect |
| 36. C2×Dic218 | C2×C4 | semidirect |
| 42. C22×Dic109 | C2×C4 | semidirect |
| 61. C2×D4×C109 | C2×C4 | semidirect |
| 102. C4×D109 | C22⋊C4 | semidirect |
| 134. C109 | #2311 | semidirect |
| 141. #390 | D109 | semidirect |
| 177. C2×D4 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182028 | 2 |
| C2×#16812656 | 2 |
| C2×C4⋊C4×D109 | 2 |
| #20294932 | 2 |
| #20294931 | 2 |
| #20294929 | 2 |
| #20294902 | 2 |
| #20294884 | 2 |
| #390×C109 | 2 |
| #2311 | 109 |