Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C22×D872 | C2 | semidirect |
| 2. C22×#13182014 | C2 | semidirect |
| 3. C2×#16812695 | C2 | semidirect |
| 4. C2×#16812661 | C2 | semidirect |
| 5. #20295220 | C2 | direct (N × H) |
| 6. C2×#16812628 | C2 | semidirect |
| 7. C2×#16812619 | C2 | semidirect |
| 8. C2×#102×C109 | C2 | semidirect |
| 15. C2×D872 | C22 | semidirect |
| 17. C2×#13182014 | C22 | semidirect |
| 20. #16812695 | C22 | semidirect |
| 22. #16812661 | C22 | semidirect |
| 25. #16812628 | C22 | semidirect |
| 26. #16812619 | C22 | semidirect |
| 30. #102×C109 | C22 | semidirect |
| 38. C2×D436 | D4 | semidirect |
| 92. C2×Dic109 | D8 | semidirect |
| 100. D436 | C2×D4 | semidirect |
| 125. Dic109 | C2×D8 | semidirect |
| 127. C2×C109 | #459 | semidirect |
| 134. C109 | C2×#459 | semidirect |
| 142. C2×#102 | D109 | semidirect |
| 164. #102 | C2×D109 | semidirect |
| 263. C2 | #20295220 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D872 | 2 |
| C22×#13182014 | 2 |
| C2×#16812695 | 2 |
| C2×#16812661 | 2 |
| #20295220 | 2 |
| C2×#16812628 | 2 |
| C2×#16812619 | 2 |
| C2×#102×C109 | 2 |
| C2×#459 | 109 |