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×#13095510 | C2 | semidirect |
| 3. #20261062 | C2 | semidirect |
| 4. #20261017 | C2 | semidirect |
| 5. #20260936 | C2 | semidirect |
| 6. #20260930 | C2 | semidirect |
| 7. #20260881 | C2 | semidirect |
| 8. #20260844 | C2 | semidirect |
| 9. #20260834 | C2 | semidirect |
| 10. #20260791 | C2 | semidirect |
| 11. #474×C97 | C2 | semidirect |
| 88. D4×C97 | #41 | semidirect |
| 114. Dic194 | #41 | semidirect |
| 145. C97 | #3115 | semidirect |
| 150. #474 | D97 | semidirect |
| 241. D4 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261286 | 2 |
| C4×#13095510 | 2 |
| #20261062 | 2 |
| #20261017 | 2 |
| #20260936 | 2 |
| #20260930 | 2 |
| #20260881 | 2 |
| #20260844 | 2 |
| #20260834 | 2 |
| #20260791 | 2 |
| #474×C97 | 2 |
| #3115 | 97 |