Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1984 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 565 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. C23×C22⋊D109 | C2 | semidirect |
| 2. #20295588 | C2 | direct (N × H) |
| 3. C2×#16812683 | C2 | semidirect |
| 4. C2×#16812673 | C2 | semidirect |
| 5. C2×#16812669 | C2 | semidirect |
| 6. C22×C22⋊C4×C109 | C2 | semidirect |
| 7. C24×D109 | C22 | semidirect |
| 8. C22×D436 | C22 | semidirect |
| 11. C22×C22⋊D109 | C22 | semidirect |
| 12. C22×C22⋊D109 | C22 | semidirect |
| 13. C23×Dic109 | C22 | semidirect |
| 14. #16812683 | C22 | semidirect |
| 15. #16812673 | C22 | semidirect |
| 16. #16812669 | C22 | semidirect |
| 17. C2×C4⋊Dic109 | C22 | semidirect |
| 18. C2×#13182006 | C22 | semidirect |
| 20. C23×C4×C109 | C22 | semidirect |
| 21. C2×C22⋊C4×C109 | C22 | semidirect |
| 22. C2×C22⋊C4×C109 | C22 | semidirect |
| 26. C23×D109 | C23 | semidirect |
| 28. C2×D436 | C23 | semidirect |
| 33. C2×C22⋊D109 | C23 | semidirect |
| 36. C22×Dic109 | C23 | semidirect |
| 37. C4⋊Dic109 | C23 | semidirect |
| 38. #13182006 | C23 | semidirect |
| 40. C24×C109 | D4 | semidirect |
| 46. C22×C4×C109 | C23 | semidirect |
| 47. C22⋊C4×C109 | C23 | semidirect |
| 54. C23×C109 | C2×D4 | semidirect |
| 91. C2×C109 | #534 | semidirect |
| 96. C109 | C2×#534 | semidirect |
| 102. C22×C22⋊C4 | D109 | semidirect |
| 111. C23×C4 | C2×D109 | semidirect |
| 117. C2×C22⋊C4 | C2×D109 | semidirect |
| 118. C2×C22⋊C4 | C2×D109 | semidirect |
| 124. C24 | D436 | semidirect |
| 140. C22×C4 | C22×D109 | semidirect |
| 143. C22⋊C4 | C22×D109 | semidirect |
| 156. C23 | C2×D436 | semidirect |
| 188. C2 | #20295588 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D109 | 2 |
| #20295588 | 2 |
| C2×#16812683 | 2 |
| C2×#16812673 | 2 |
| C2×#16812669 | 2 |
| C22×C22⋊C4×C109 | 2 |
| C2×#534 | 109 |