Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#16812778 | C2 | semidirect |
| 2. #20296005 | C2 | direct (N × H) |
| 3. C2×#16812758 | C2 | semidirect |
| 4. C2×#16812757 | C2 | semidirect |
| 7. #16812778 | C22 | semidirect |
| 11. #16812758 | C22 | semidirect |
| 12. #16812757 | C22 | semidirect |
| 16. C2×#13182029 | C4 | semidirect |
| 18. C22×Dic218 | C4 | semidirect |
| 20. C22×C22⋊D109 | C4 | semidirect |
| 22. C22×C4×D109 | C4 | semidirect |
| 24. C23×C4×C109 | C4 | semidirect |
| 38. C2×Dic218 | C2×C4 | semidirect |
| 48. C2×C22⋊D109 | C2×C4 | semidirect |
| 56. C2×C4×D109 | C2×C4 | semidirect |
| 67. C22×C4×C109 | C2×C4 | semidirect |
| 138. C2×C109 | #410 | semidirect |
| 144. C109 | C2×#410 | semidirect |
| 161. C23×C4 | #89137 | semidirect |
| 207. C22×C4 | C2×#89137 | semidirect |
| 285. C2 | #20296005 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812778 | 2 |
| #20296005 | 2 |
| C2×#16812758 | 2 |
| C2×#16812757 | 2 |
| C22×#13182029 | 2 |
| C2×#410 | 109 |