Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#16812705 | C2 | semidirect |
| 3. C2×#16812626 | C2 | semidirect |
| 4. C2×#16812625 | C2 | semidirect |
| 5. #20294790 | C2 | semidirect |
| 6. #20294780 | C2 | semidirect |
| 7. #408×C109 | C2 | semidirect |
| 11. C2×#13182019 | C4 | semidirect |
| 12. C2×#13182017 | C4 | semidirect |
| 13. C2×#13182016 | C4 | semidirect |
| 14. C2×#13182014 | C4 | semidirect |
| 131. C109 | #1876 | semidirect |
| 136. #408 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812719 | 2 |
| C2×#16812705 | 2 |
| C2×#16812626 | 2 |
| C2×#16812625 | 2 |
| #20294790 | 2 |
| #20294780 | 2 |
| #408×C109 | 2 |
| #1876 | 109 |