Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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. #20261217 | C2 | semidirect |
| 3. #20261213 | C2 | semidirect |
| 4. #20261209 | C2 | semidirect |
| 5. C4×#13095512 | C2 | semidirect |
| 6. #117×D97 | C2 | semidirect |
| 7. #519×C97 | C2 | semidirect |
| 8. C2×#13095512 | C4 | semidirect |
| 13. Q8×Dic97 | C22 | semidirect |
| 14. C4×D388 | C22 | semidirect |
| 15. #15690772 | C22 | semidirect |
| 17. #15690768 | C22 | semidirect |
| 18. #15690767 | C22 | semidirect |
| 20. C4⋊C4×D97 | C22 | semidirect |
| 22. C42×D97 | C22 | semidirect |
| 24. C4×Q8×C97 | C22 | semidirect |
| 27. #13095512 | C2×C4 | semidirect |
| 28. #13095512 | C2×C4 | semidirect |
| 29. C2×D388 | C2×C4 | semidirect |
| 32. C2×C4×D97 | C2×C4 | semidirect |
| 42. C2×Q8×C97 | C2×C4 | semidirect |
| 80. C97 | #3428 | semidirect |
| 84. #519 | D97 | semidirect |
| 95. C4×Q8 | C2×D97 | semidirect |
| 109. C2×Q8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095512 | 2 |
| #20261217 | 2 |
| #20261213 | 2 |
| #20261209 | 2 |
| C4×#13095512 | 2 |
| #117×D97 | 2 |
| #519×C97 | 2 |
| #3428 | 97 |