Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #20295697 | C2 | semidirect |
| 2. D4×Dic218 | C2 | semidirect |
| 3. #20295373 | C2 | semidirect |
| 4. #20295371 | C2 | semidirect |
| 5. #20295306 | C2 | semidirect |
| 6. #20295305 | C2 | semidirect |
| 7. #20295221 | C2 | semidirect |
| 8. #20295219 | C2 | semidirect |
| 9. C8×Dic218 | C2 | semidirect |
| 10. #20295106 | C2 | semidirect |
| 11. C4×D8×C109 | C2 | semidirect |
| 81. D4×C109 | #41 | semidirect |
| 102. Dic218 | D8 | semidirect |
| 132. C109 | #3358 | semidirect |
| 143. C4×D8 | D109 | semidirect |
| 222. D4 | #13182029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295697 | 2 |
| D4×Dic218 | 2 |
| #20295373 | 2 |
| #20295371 | 2 |
| #20295306 | 2 |
| #20295305 | 2 |
| #20295221 | 2 |
| #20295219 | 2 |
| C8×Dic218 | 2 |
| #20295106 | 2 |
| C4×D8×C109 | 2 |
| #3358 | 109 |