Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20295434 | C2 | semidirect |
| 4. #20295433 | C2 | semidirect |
| 5. #20295427 | C2 | semidirect |
| 6. #20295426 | C2 | semidirect |
| 48. #13182013 | Q8 | semidirect |
| 72. M16×C109 | Q8 | semidirect |
| 125. C109 | #3166 | semidirect |
| 176. M16 | Dic218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295579 | 2 |
| C2×#16812690 | 2 |
| #20295434 | 2 |
| #20295433 | 2 |
| #20295427 | 2 |
| #20295426 | 2 |
| #20295069 | 2 |
| #20295068 | 2 |
| #20295066 | 2 |
| M16×Dic109 | 2 |
| #428×C109 | 2 |
| #3166 | 109 |