Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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×#16812729 | C2 | semidirect |
| 2. C2×#16812678 | C2 | semidirect |
| 3. #20295188 | C2 | semidirect |
| 4. #20295182 | C2 | semidirect |
| 5. #20295177 | C2 | semidirect |
| 6. #20295027 | C2 | semidirect |
| 7. #20294990 | C2 | semidirect |
| 9. C22×Dic218 | C22 | semidirect |
| 11. C2×#13182019 | C22 | semidirect |
| 12. C2×#13182017 | C22 | semidirect |
| 13. C2×#13182013 | C22 | semidirect |
| 17. #16812678 | C22 | semidirect |
| 18. C2×C4⋊Dic109 | C22 | semidirect |
| 21. #16812623 | C22 | semidirect |
| 22. #16812620 | C22 | semidirect |
| 24. C22⋊#11724784 | C22 | semidirect |
| 130. C22×C109 | #137 | semidirect |
| 147. C109 | #3007 | semidirect |
| 277. C22 | #16812729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812729 | 2 |
| C2×#16812678 | 2 |
| #20295188 | 2 |
| #20295182 | 2 |
| #20295177 | 2 |
| #20295027 | 2 |
| #20294990 | 2 |
| C22×#41×C109 | 2 |
| #3007 | 109 |