Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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. #20260808 | C2 | semidirect |
| 3. #20260805 | C2 | semidirect |
| 4. C8×D388 | C2 | semidirect |
| 5. #20260800 | C2 | semidirect |
| 6. #20260796 | C2 | semidirect |
| 7. #20260700 | C2 | semidirect |
| 8. C22⋊C8×D97 | C2 | semidirect |
| 9. #433×C97 | C2 | semidirect |
| 12. C2×#13095494 | C22 | semidirect |
| 15. C2×C8×D97 | C22 | semidirect |
| 22. C4⋊#11715895 | C22 | semidirect |
| 26. #15690722 | C22 | semidirect |
| 27. #15690722 | C22 | semidirect |
| 28. #15690721 | C22 | semidirect |
| 29. C4×#11715895 | C22 | semidirect |
| 31. C4⋊C8×C97 | C22 | semidirect |
| 33. #97×C97 | C22 | semidirect |
| 34. C4×C8×C97 | C22 | semidirect |
| 115. C97 | #2977 | semidirect |
| 122. #433 | D97 | semidirect |
| 139. C4⋊C8 | C2×D97 | semidirect |
| 147. #97 | C2×D97 | semidirect |
| 149. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261247 | 2 |
| #20260808 | 2 |
| #20260805 | 2 |
| C8×D388 | 2 |
| #20260800 | 2 |
| #20260796 | 2 |
| #20260700 | 2 |
| C22⋊C8×D97 | 2 |
| #433×C97 | 2 |
| #2977 | 97 |