Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 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. #20261292 | C2 | semidirect |
| 3. #20261036 | C2 | semidirect |
| 4. #20261026 | C2 | semidirect |
| 5. #20261016 | C2 | semidirect |
| 6. #20260777 | C2 | semidirect |
| 8. #423×C97 | C2 | semidirect |
| 11. #15690810 | C22 | semidirect |
| 12. #15690810 | C22 | semidirect |
| 13. #15690802 | C22 | semidirect |
| 25. #15690744 | C22 | semidirect |
| 26. #15690742 | C22 | semidirect |
| 31. C4⋊C8×C97 | C22 | semidirect |
| 32. C4⋊C8×C97 | C22 | semidirect |
| 38. C2×D388 | Q8 | semidirect |
| 116. C97 | #3077 | semidirect |
| 123. #423 | D97 | semidirect |
| 145. C4⋊C8 | C2×D97 | semidirect |
| 146. C4⋊C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261292 | 2 |
| C2×C4×D388 | 2 |
| #20261036 | 2 |
| #20261026 | 2 |
| #20261016 | 2 |
| #20260777 | 2 |
| #20260741 | 2 |
| #423×C97 | 2 |
| #3077 | 97 |