Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #20295043 | C2 | semidirect |
| 3. #20295032 | C2 | semidirect |
| 4. C2×#16812615 | C2 | semidirect |
| 5. #20294798 | C2 | semidirect |
| 6. #20294784 | C2 | semidirect |
| 7. #568×C109 | C2 | semidirect |
| 11. C2×#13182016 | C4 | semidirect |
| 12. C2×#13182014 | C4 | semidirect |
| 113. C109 | #1903 | semidirect |
| 115. #568 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812724 | 2 |
| #20295043 | 2 |
| #20295032 | 2 |
| C2×#16812615 | 2 |
| #20294798 | 2 |
| #20294784 | 2 |
| #568×C109 | 2 |
| #1903 | 109 |