Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #20295360 | C2 | semidirect |
| 4. #20295318 | C2 | semidirect |
| 5. #20295266 | C2 | semidirect |
| 6. #20295233 | C2 | semidirect |
| 7. #20295183 | C2 | semidirect |
| 8. C4×Dic436 | C2 | semidirect |
| 10. #103×D109 | C2 | semidirect |
| 11. #487×C109 | C2 | semidirect |
| 90. D436 | Q16 | semidirect |
| 123. C109 | #3299 | semidirect |
| 126. #487 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295737 | 2 |
| #20295691 | 2 |
| #20295360 | 2 |
| #20295318 | 2 |
| #20295266 | 2 |
| #20295233 | 2 |
| #20295183 | 2 |
| C4×Dic436 | 2 |
| C8×D436 | 2 |
| #103×D109 | 2 |
| #487×C109 | 2 |
| #3299 | 109 |