Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 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. #20295652 | C2 | direct (N × H) |
| 2. C2×#16812678 | C2 | semidirect |
| 3. C2×#16812676 | C2 | semidirect |
| 6. C22×Dic218 | C22 | semidirect |
| 8. #16812678 | C22 | semidirect |
| 9. #16812676 | C22 | semidirect |
| 10. C2×C4⋊Dic109 | C22 | semidirect |
| 11. C2×#13182008 | C22 | semidirect |
| 20. C2×Dic218 | C23 | semidirect |
| 24. C4⋊Dic109 | C23 | semidirect |
| 25. #13182008 | C23 | semidirect |
| 29. C24×C109 | Q8 | semidirect |
| 43. C23×C109 | C2×Q8 | semidirect |
| 68. C2×C109 | #543 | semidirect |
| 72. C109 | C2×#543 | semidirect |
| 92. C24 | Dic218 | semidirect |
| 115. C23 | C2×Dic218 | semidirect |
| 140. C2 | #20295652 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295652 | 2 |
| C2×#16812678 | 2 |
| C2×#16812676 | 2 |
| C22×C22⋊Dic109 | 2 |
| C22×C22⋊C4×C109 | 2 |
| C2×#543 | 109 |