Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16812730 | C2 | semidirect |
| 3. C2×#16812688 | C2 | semidirect |
| 4. C2×#16812625 | C2 | semidirect |
| 5. C2×#16812615 | C2 | semidirect |
| 6. #20294785 | C2 | semidirect |
| 7. #419×C109 | C2 | semidirect |
| 49. #13182013 | D4 | semidirect |
| 54. C4×Dic109 | D4 | semidirect |
| 60. C2×Q8×C109 | D4 | semidirect |
| 132. C109 | #2004 | semidirect |
| 137. #419 | D109 | semidirect |
| 172. C2×Q8 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| #20295595 | 2 |
| C2×#16812688 | 2 |
| C2×#16812625 | 2 |
| C2×#16812615 | 2 |
| #20294785 | 2 |
| #419×C109 | 2 |
| #2004 | 109 |