Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20295066 | C2 | semidirect |
| 3. C2×#16812627 | C2 | semidirect |
| 4. #20295025 | C2 | semidirect |
| 5. C2×#16812616 | C2 | semidirect |
| 6. #20294786 | C2 | semidirect |
| 7. #390×C109 | C2 | semidirect |
| 40. #13182013 | D4 | semidirect |
| 131. C109 | #2037 | semidirect |
| 137. #390 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295593 | 2 |
| #20295066 | 2 |
| C2×#16812627 | 2 |
| #20295025 | 2 |
| C2×#16812616 | 2 |
| #20294786 | 2 |
| #390×C109 | 2 |
| #2037 | 109 |