Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812690 | C2 | semidirect |
| 3. #20295389 | C2 | direct (N × H) |
| 4. C2×#16812621 | C2 | semidirect |
| 5. C2×#16812620 | C2 | semidirect |
| 6. C2×#16812619 | C2 | semidirect |
| 7. C2×#16812609 | C2 | semidirect |
| 8. C2×#102×C109 | C2 | semidirect |
| 16. #16812690 | C22 | semidirect |
| 21. #16812621 | C22 | semidirect |
| 22. #16812620 | C22 | semidirect |
| 23. #16812619 | C22 | semidirect |
| 24. #16812609 | C22 | semidirect |
| 28. #102×C109 | C22 | semidirect |
| 111. C2×C109 | #490 | semidirect |
| 117. C109 | C2×#490 | semidirect |
| 124. C2×#102 | D109 | semidirect |
| 144. #102 | C2×D109 | semidirect |
| 229. C2 | #20295389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812695 | 2 |
| C2×#16812690 | 2 |
| #20295389 | 2 |
| C2×#16812621 | 2 |
| C2×#16812620 | 2 |
| C2×#16812619 | 2 |
| C2×#16812609 | 2 |
| C2×#102×C109 | 2 |
| C2×#490 | 109 |