Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13182019 | C2 | semidirect |
| 2. C22×#13182017 | C2 | semidirect |
| 3. C2×#16812678 | C2 | semidirect |
| 4. #20295188 | C2 | direct (N × H) |
| 5. C2×#16812623 | C2 | semidirect |
| 6. C2×#16812620 | C2 | semidirect |
| 7. C2×C22⋊#11724784 | C2 | semidirect |
| 11. C2×#13182019 | C22 | semidirect |
| 13. C2×#13182017 | C22 | semidirect |
| 17. #16812678 | C22 | semidirect |
| 21. #16812623 | C22 | semidirect |
| 22. #16812620 | C22 | semidirect |
| 23. C22⋊#11724784 | C22 | semidirect |
| 131. C2×C109 | #452 | semidirect |
| 136. C109 | C2×#452 | semidirect |
| 267. C2 | #20295188 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182019 | 2 |
| C22×#13182017 | 2 |
| C2×#16812678 | 2 |
| #20295188 | 2 |
| C2×#16812623 | 2 |
| C2×#16812620 | 2 |
| C2×C22⋊#11724784 | 2 |
| C22×#41×C109 | 2 |
| C2×#452 | 109 |