Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D109 | C2 | semidirect |
| 3. C2×#16812626 | C2 | semidirect |
| 4. C4×#13182006 | C2 | semidirect |
| 5. #20294787 | C2 | semidirect |
| 6. #20294786 | C2 | semidirect |
| 7. C2×#104×C109 | C2 | semidirect |
| 15. #16812675 | C4 | semidirect |
| 16. #16812675 | C4 | semidirect |
| 17. #16812670 | C4 | semidirect |
| 18. #16812670 | C4 | semidirect |
| 45. #13182013 | D4 | semidirect |
| 73. M16×C109 | D4 | semidirect |
| 139. C2×D109 | #104 | semidirect |
| 160. C109 | #1871 | semidirect |
| 164. C2×#104 | D109 | semidirect |
| 218. M16 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D109 | 2 |
| #20295533 | 2 |
| C2×#16812626 | 2 |
| C4×#13182006 | 2 |
| #20294787 | 2 |
| #20294786 | 2 |
| C2×#104×C109 | 2 |
| #1871 | 109 |