Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15690838 | C2 | semidirect |
| 2. #20261285 | C2 | semidirect |
| 3. C2×C4×D388 | C2 | semidirect |
| 4. #20260951 | C2 | semidirect |
| 5. #20260941 | C2 | semidirect |
| 6. #20260931 | C2 | semidirect |
| 7. #20260737 | C2 | semidirect |
| 8. #423×C97 | C2 | semidirect |
| 15. #15690810 | C22 | semidirect |
| 16. #15690807 | C22 | semidirect |
| 17. #15690798 | C22 | semidirect |
| 28. #15690735 | C22 | semidirect |
| 29. #15690732 | C22 | semidirect |
| 32. C4⋊C8×C97 | C22 | semidirect |
| 33. C4⋊C8×C97 | C22 | semidirect |
| 42. C2×D388 | D4 | semidirect |
| 118. C4×C97 | AGL(1,ℤ/8) | semidirect |
| 130. C97 | #3036 | semidirect |
| 137. #423 | D97 | semidirect |
| 160. C4⋊C8 | C2×D97 | semidirect |
| 161. C4⋊C8 | C2×D97 | semidirect |
| 250. C4 | #15690838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690838 | 2 |
| #20261285 | 2 |
| C2×C4×D388 | 2 |
| #20260951 | 2 |
| #20260941 | 2 |
| #20260931 | 2 |
| #20260737 | 2 |
| #423×C97 | 2 |
| #3036 | 97 |