Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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×Dic436 | C2 | semidirect |
| 2. #20295466 | C2 | direct (N × H) |
| 3. C2×#16812645 | C2 | semidirect |
| 4. C2×#16812643 | C2 | semidirect |
| 5. C2×#16812639 | C2 | semidirect |
| 11. C2×Dic436 | C22 | semidirect |
| 12. #16812645 | C22 | semidirect |
| 13. #16812643 | C22 | semidirect |
| 14. #16812639 | C22 | semidirect |
| 81. C2×C109 | #510 | semidirect |
| 84. C109 | C2×#510 | semidirect |
| 165. C2 | #20295466 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic436 | 2 |
| #20295466 | 2 |
| C2×#16812645 | 2 |
| C2×#16812643 | 2 |
| C2×#16812639 | 2 |
| C2×#135×C109 | 2 |
| C2×#510 | 109 |