Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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×#16812644 | C2 | semidirect |
| 3. #20295410 | C2 | semidirect |
| 4. C4×D872 | C2 | semidirect |
| 5. #20294831 | C2 | semidirect |
| 6. #20294828 | C2 | semidirect |
| 7. C4⋊C16×C109 | C2 | semidirect |
| 77. C109 | #2210 | semidirect |
| 82. C4⋊C16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812644 | 2 |
| C2×D1744 | 2 |
| #20295410 | 2 |
| C4×D872 | 2 |
| #20294831 | 2 |
| #20294828 | 2 |
| C4⋊C16×C109 | 2 |
| #2210 | 109 |