Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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 |
|---|---|---|
| 1. C2×#16812724 | C2 | semidirect |
| 2. C22×#13182014 | C2 | semidirect |
| 3. #20295500 | C2 | semidirect |
| 4. #20295238 | C2 | semidirect |
| 5. #20295218 | C2 | semidirect |
| 6. #20295053 | C2 | semidirect |
| 7. #20295031 | C2 | semidirect |
| 8. #20295022 | C2 | semidirect |
| 9. #535×C109 | C2 | semidirect |
| 12. C2×#13182016 | C22 | semidirect |
| 15. C2×#13182014 | C22 | semidirect |
| 18. C4×D436 | C22 | semidirect |
| 22. C4⋊#11724784 | C22 | semidirect |
| 23. #16812623 | C22 | semidirect |
| 24. #16812620 | C22 | semidirect |
| 25. #16812620 | C22 | semidirect |
| 28. #127×C109 | C22 | semidirect |
| 29. #124×C109 | C22 | semidirect |
| 36. C2×D436 | D4 | semidirect |
| 122. C109 | #3041 | semidirect |
| 125. #535 | D109 | semidirect |
| 142. #127 | C2×D109 | semidirect |
| 143. #124 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812724 | 2 |
| C22×#13182014 | 2 |
| #20295500 | 2 |
| #20295238 | 2 |
| #20295218 | 2 |
| #20295053 | 2 |
| #20295031 | 2 |
| #20295022 | 2 |
| #535×C109 | 2 |
| #3041 | 109 |