Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20261286 | C2 | semidirect |
| 2. C4×#13095512 | C2 | semidirect |
| 3. #20261061 | C2 | semidirect |
| 4. #20261012 | C2 | semidirect |
| 5. #20260935 | C2 | semidirect |
| 6. #20260931 | C2 | semidirect |
| 7. #20260883 | C2 | semidirect |
| 8. #20260846 | C2 | semidirect |
| 9. #20260838 | C2 | semidirect |
| 10. #20260791 | C2 | semidirect |
| 11. #475×C97 | C2 | semidirect |
| 88. Q8×C97 | #41 | semidirect |
| 106. D388 | #41 | semidirect |
| 145. C97 | #3115 | semidirect |
| 149. #475 | D97 | semidirect |
| 233. Q8 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261286 | 2 |
| C4×#13095512 | 2 |
| #20261061 | 2 |
| #20261012 | 2 |
| #20260935 | 2 |
| #20260931 | 2 |
| #20260883 | 2 |
| #20260846 | 2 |
| #20260838 | 2 |
| #20260791 | 2 |
| #475×C97 | 2 |
| #3115 | 97 |