Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#16812730 | C2 | semidirect |
| 3. C4×#13182029 | C2 | semidirect |
| 4. #20295245 | C2 | semidirect |
| 5. #20295238 | C2 | semidirect |
| 6. #20295050 | C2 | semidirect |
| 7. #20295035 | C2 | semidirect |
| 8. #20295031 | C2 | semidirect |
| 9. C2×#124×C109 | C2 | semidirect |
| 13. C2×#13182019 | C22 | semidirect |
| 15. C2×#13182016 | C22 | semidirect |
| 19. C4×Dic218 | C22 | semidirect |
| 20. C4×D436 | C22 | semidirect |
| 25. C4⋊#11724784 | C22 | semidirect |
| 26. #16812623 | C22 | semidirect |
| 126. C109 | #3040 | semidirect |
| 129. C2×#124 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| C2×#16812725 | 2 |
| C4×#13182029 | 2 |
| #20295245 | 2 |
| #20295238 | 2 |
| #20295050 | 2 |
| #20295035 | 2 |
| #20295031 | 2 |
| C2×#124×C109 | 2 |
| #3040 | 109 |