Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #20295433 | C2 | semidirect |
| 3. #20295426 | C2 | semidirect |
| 4. #20295423 | C2 | semidirect |
| 29. #13182013 | Q8 | semidirect |
| 43. C2×C8×C109 | Q8 | semidirect |
| 76. C109 | #3163 | semidirect |
| 109. C2×C8 | Dic218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295657 | 2 |
| #20295433 | 2 |
| #20295426 | 2 |
| #20295423 | 2 |
| #20295066 | 2 |
| #20295064 | 2 |
| #20294981 | 2 |
| C2×#106×C109 | 2 |
| #3163 | 109 |