Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13095501 | C2 | semidirect |
| 3. #20261309 | C2 | semidirect |
| 4. #20260894 | C2 | semidirect |
| 5. #20260889 | C2 | semidirect |
| 6. #20260745 | C2 | semidirect |
| 7. #20260731 | C2 | semidirect |
| 8. #20260703 | C2 | semidirect |
| 9. C2×#137×C97 | C2 | semidirect |
| 141. C97 | #3011 | semidirect |
| 143. C2×#137 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690857 | 2 |
| C22×#13095501 | 2 |
| #20261309 | 2 |
| #20260894 | 2 |
| #20260889 | 2 |
| #20260745 | 2 |
| #20260731 | 2 |
| #20260703 | 2 |
| C2×#137×C97 | 2 |
| #3011 | 97 |